[{"publication_status":"published","publication_identifier":{"issn":["0294-1449","1873-1430"]},"issue":"6","year":"2019","citation":{"ama":"Winkler M. Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 2019;36(6):1747-1790. doi:10.1016/j.anihpc.2019.02.004","ieee":"M. Winkler, “Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation,” Annales de l’Institut Henri Poincaré C, Analyse non linéaire, vol. 36, no. 6, pp. 1747–1790, 2019, doi: 10.1016/j.anihpc.2019.02.004.","chicago":"Winkler, Michael. “Global Solvability and Stabilization in a Two-Dimensional Cross-Diffusion System Modeling Urban Crime Propagation.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 36, no. 6 (2019): 1747–90. https://doi.org/10.1016/j.anihpc.2019.02.004.","apa":"Winkler, M. (2019). Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation. Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 36(6), 1747–1790. https://doi.org/10.1016/j.anihpc.2019.02.004","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 36 (2019) 1747–1790.","bibtex":"@article{Winkler_2019, title={Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation}, volume={36}, DOI={10.1016/j.anihpc.2019.02.004}, number={6}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2019}, pages={1747–1790} }","mla":"Winkler, Michael. “Global Solvability and Stabilization in a Two-Dimensional Cross-Diffusion System Modeling Urban Crime Propagation.” Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, vol. 36, no. 6, European Mathematical Society - EMS - Publishing House GmbH, 2019, pp. 1747–90, doi:10.1016/j.anihpc.2019.02.004."},"page":"1747-1790","intvolume":" 36","publisher":"European Mathematical Society - EMS - Publishing House GmbH","date_updated":"2025-12-19T10:58:37Z","author":[{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-19T10:58:29Z","volume":36,"title":"Global solvability and stabilization in a two-dimensional cross-diffusion system modeling urban crime propagation","doi":"10.1016/j.anihpc.2019.02.004","type":"journal_article","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","abstract":[{"lang":"eng","text":"The system\r\n \r\n \r\n \\left\\{\\begin{matrix} u_{t} = \\mathrm{\\Delta }u−\\chi \\mathrm{∇} \\cdot \\left(\\frac{u}{v}\\mathrm{∇}v\\right)−uv + B_{1}(x,t), \\\\ v_{t} = \\mathrm{\\Delta }v + uv−v + B_{2}(x,t), \\\\ \\end{matrix}\\right.\\:\\:( \\star )\r\n \r\n \r\n \r\n is considered in a disk \r\n \r\n \\mathrm{\\Omega } \\subset \\mathbb{R}^{2}\r\n \r\n , with a positive parameter \r\n \r\n χ\r\n \r\n and given nonnegative and suitably regular functions \r\n \r\n B_{1}\r\n \r\n and \r\n \r\n B_{2}\r\n \r\n defined on \r\n \r\n \\mathrm{\\Omega } \\times (0,\\infty )\r\n \r\n . In the particular version obtained when \r\n \r\n \\chi = 2\r\n \r\n , (\r\n \r\n \\star\r\n \r\n ) was proposed in [31] as a model for crime propagation in urban regions.\r\n \r\n \r\n Within a suitable generalized framework, it is shown that under mild assumptions on the parameter functions and the initial data the no-flux initial-boundary value problem for (\r\n \r\n \\star\r\n \r\n ) possesses at least one global solution in the case when all model ingredients are radially symmetric with respect to the center of \r\n \r\n Ω\r\n \r\n . Moreover, under an additional hypothesis on stabilization of the given external source terms in both equations, these solutions are shown to approach the solution of an elliptic boundary value problem in an appropriate sense.\r\n \r\n The analysis is based on deriving a priori estimates for a family of approximate problems, in a first step achieving some spatially global but weak initial regularity information which in a series of spatially localized arguments is thereafter successively improved.\r\n \r\n To the best of our knowledge, this is the first result on global existence of solutions to the two-dimensional version of the full original system (\r\n \r\n \\star\r\n \r\n ) for arbitrarily large values of \r\n \r\n χ\r\n \r\n .\r\n "}],"status":"public","_id":"63362","user_id":"31496","language":[{"iso":"eng"}]},{"issue":"03","publication_status":"published","publication_identifier":{"issn":["0218-2025","1793-6314"]},"citation":{"mla":"Winkler, Michael. “Global Generalized Solutions to a Multi-Dimensional Doubly Tactic Resource Consumption Model Accounting for Social Interactions.” Mathematical Models and Methods in Applied Sciences, vol. 29, no. 03, World Scientific Pub Co Pte Ltd, 2019, pp. 373–418, doi:10.1142/s021820251950012x.","bibtex":"@article{Winkler_2019, title={Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions}, volume={29}, DOI={10.1142/s021820251950012x}, number={03}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2019}, pages={373–418} }","short":"M. Winkler, Mathematical Models and Methods in Applied Sciences 29 (2019) 373–418.","apa":"Winkler, M. (2019). Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Mathematical Models and Methods in Applied Sciences, 29(03), 373–418. https://doi.org/10.1142/s021820251950012x","ieee":"M. Winkler, “Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions,” Mathematical Models and Methods in Applied Sciences, vol. 29, no. 03, pp. 373–418, 2019, doi: 10.1142/s021820251950012x.","chicago":"Winkler, Michael. “Global Generalized Solutions to a Multi-Dimensional Doubly Tactic Resource Consumption Model Accounting for Social Interactions.” Mathematical Models and Methods in Applied Sciences 29, no. 03 (2019): 373–418. https://doi.org/10.1142/s021820251950012x.","ama":"Winkler M. Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions. Mathematical Models and Methods in Applied Sciences. 2019;29(03):373-418. doi:10.1142/s021820251950012x"},"intvolume":" 29","page":"373-418","year":"2019","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"date_created":"2025-12-19T10:59:03Z","volume":29,"date_updated":"2025-12-19T10:59:10Z","publisher":"World Scientific Pub Co Pte Ltd","doi":"10.1142/s021820251950012x","title":"Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions","type":"journal_article","publication":"Mathematical Models and Methods in Applied Sciences","status":"public","abstract":[{"text":" This work is concerned with a prototypical model for the spatio-temporal evolution of a forager–exploiter system, consisting of two species which simultaneously consume a common nutrient, and which interact through a taxis-type mechanism according to which individuals from the exploiter subpopulation move upward density gradients of the forager subgroup. Specifically, the model [Formula: see text] for the population densities [Formula: see text] and [Formula: see text] of foragers and exploiters, as well as the nutrient concentration [Formula: see text], is considered in smoothly bounded domains [Formula: see text], [Formula: see text]. It is first shown that under an explicit condition linking the sizes of the resource production rate [Formula: see text] and of the initial nutrient concentration, an associated Neumann-type initial-boundary value problem admits a global solution within an appropriate generalized concept. The second of the main results asserts stabilization of these solutions toward spatially homogeneous equilibria in the large time limit, provided that [Formula: see text] satisfies a mild assumption on temporal decay. To the best of our knowledge, these are the first rigorous analytical results addressing taxis-type cross-diffusion mechanisms coupled in a cascade-like manner as in (⋆). ","lang":"eng"}],"user_id":"31496","_id":"63363","language":[{"iso":"eng"}]},{"status":"public","type":"journal_article","publication":"Nonlinear Analysis","language":[{"iso":"eng"}],"user_id":"31496","_id":"63366","citation":{"ama":"Winkler M. Instantaneous regularization of distributions from<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\" id=\"d1e19\" altimg=\"si17.gif\"><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>in the one-dimensional parabolic Keller–Segel system. Nonlinear Analysis. 2019;183:102-116. doi:10.1016/j.na.2019.01.017","ieee":"M. Winkler, “Instantaneous regularization of distributions from<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\" id=\"d1e19\" altimg=\"si17.gif\"><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>in the one-dimensional parabolic Keller–Segel system,” Nonlinear Analysis, vol. 183, pp. 102–116, 2019, doi: 10.1016/j.na.2019.01.017.","chicago":"Winkler, Michael. “Instantaneous Regularization of Distributions From<mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Display=\"inline\" Overflow=\"scroll\" Id=\"d1e19\" Altimg=\"si17.Gif\"><mml:Msup><mml:Mrow><mml:Mrow><mml:Mo>(</Mml:Mo><mml:Msup><mml:Mrow><mml:Mi>C</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mn>0</Mml:Mn></Mml:Mrow></Mml:Msup><mml:Mo>)</Mml:Mo></Mml:Mrow></Mml:Mrow><mml:Mrow><mml:Mo>⋆</Mml:Mo></Mml:Mrow></Mml:Msup><mml:Mo>×</Mml:Mo><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mn>2</Mml:Mn></Mml:Mrow></Mml:Msup></Mml:Math>in the One-Dimensional Parabolic Keller–Segel System.” Nonlinear Analysis 183 (2019): 102–16. https://doi.org/10.1016/j.na.2019.01.017.","apa":"Winkler, M. (2019). Instantaneous regularization of distributions from<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\" id=\"d1e19\" altimg=\"si17.gif\"><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>in the one-dimensional parabolic Keller–Segel system. Nonlinear Analysis, 183, 102–116. https://doi.org/10.1016/j.na.2019.01.017","short":"M. Winkler, Nonlinear Analysis 183 (2019) 102–116.","mla":"Winkler, Michael. “Instantaneous Regularization of Distributions From<mml:Math Xmlns:Mml=\"http://Www.W3.Org/1998/Math/MathML\" Display=\"inline\" Overflow=\"scroll\" Id=\"d1e19\" Altimg=\"si17.Gif\"><mml:Msup><mml:Mrow><mml:Mrow><mml:Mo>(</Mml:Mo><mml:Msup><mml:Mrow><mml:Mi>C</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mn>0</Mml:Mn></Mml:Mrow></Mml:Msup><mml:Mo>)</Mml:Mo></Mml:Mrow></Mml:Mrow><mml:Mrow><mml:Mo>⋆</Mml:Mo></Mml:Mrow></Mml:Msup><mml:Mo>×</Mml:Mo><mml:Msup><mml:Mrow><mml:Mi>L</Mml:Mi></Mml:Mrow><mml:Mrow><mml:Mn>2</Mml:Mn></Mml:Mrow></Mml:Msup></Mml:Math>in the One-Dimensional Parabolic Keller–Segel System.” Nonlinear Analysis, vol. 183, Elsevier BV, 2019, pp. 102–16, doi:10.1016/j.na.2019.01.017.","bibtex":"@article{Winkler_2019, title={Instantaneous regularization of distributions from<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\" id=\"d1e19\" altimg=\"si17.gif\"><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>⋆</mml:mo></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>in the one-dimensional parabolic Keller–Segel system}, volume={183}, DOI={10.1016/j.na.2019.01.017}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2019}, pages={102–116} }"},"page":"102-116","intvolume":" 183","year":"2019","publication_status":"published","publication_identifier":{"issn":["0362-546X"]},"doi":"10.1016/j.na.2019.01.017","title":"Instantaneous regularization of distributions from(C0)⋆×L2in the one-dimensional parabolic Keller–Segel system","author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-19T11:01:12Z","volume":183,"date_updated":"2025-12-19T11:01:21Z","publisher":"Elsevier BV"},{"year":"2019","citation":{"apa":"Wang, Y., Winkler, M., & Xiang, Z. (2019). The fast signal diffusion limit in Keller–Segel(-fluid) systems. Calculus of Variations and Partial Differential Equations, 58(6), Article 196. https://doi.org/10.1007/s00526-019-1656-3","bibtex":"@article{Wang_Winkler_Xiang_2019, title={The fast signal diffusion limit in Keller–Segel(-fluid) systems}, volume={58}, DOI={10.1007/s00526-019-1656-3}, number={6196}, journal={Calculus of Variations and Partial Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Wang, Yulan and Winkler, Michael and Xiang, Zhaoyin}, year={2019} }","mla":"Wang, Yulan, et al. “The Fast Signal Diffusion Limit in Keller–Segel(-Fluid) Systems.” Calculus of Variations and Partial Differential Equations, vol. 58, no. 6, 196, Springer Science and Business Media LLC, 2019, doi:10.1007/s00526-019-1656-3.","short":"Y. Wang, M. Winkler, Z. Xiang, Calculus of Variations and Partial Differential Equations 58 (2019).","chicago":"Wang, Yulan, Michael Winkler, and Zhaoyin Xiang. “The Fast Signal Diffusion Limit in Keller–Segel(-Fluid) Systems.” Calculus of Variations and Partial Differential Equations 58, no. 6 (2019). https://doi.org/10.1007/s00526-019-1656-3.","ieee":"Y. Wang, M. Winkler, and Z. Xiang, “The fast signal diffusion limit in Keller–Segel(-fluid) systems,” Calculus of Variations and Partial Differential Equations, vol. 58, no. 6, Art. no. 196, 2019, doi: 10.1007/s00526-019-1656-3.","ama":"Wang Y, Winkler M, Xiang Z. The fast signal diffusion limit in Keller–Segel(-fluid) systems. Calculus of Variations and Partial Differential Equations. 2019;58(6). doi:10.1007/s00526-019-1656-3"},"intvolume":" 58","publication_status":"published","publication_identifier":{"issn":["0944-2669","1432-0835"]},"issue":"6","title":"The fast signal diffusion limit in Keller–Segel(-fluid) systems","doi":"10.1007/s00526-019-1656-3","date_updated":"2025-12-19T10:57:05Z","publisher":"Springer Science and Business Media LLC","author":[{"full_name":"Wang, Yulan","last_name":"Wang","first_name":"Yulan"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"},{"full_name":"Xiang, Zhaoyin","last_name":"Xiang","first_name":"Zhaoyin"}],"date_created":"2025-12-19T10:56:58Z","volume":58,"status":"public","type":"journal_article","publication":"Calculus of Variations and Partial Differential Equations","article_number":"196","language":[{"iso":"eng"}],"_id":"63359","user_id":"31496"},{"year":"2019","intvolume":" 198","page":"1615-1637","citation":{"ieee":"M. Winkler, “How strong singularities can be regularized by logistic degradation in the Keller–Segel system?,” Annali di Matematica Pura ed Applicata (1923 -), vol. 198, no. 5, pp. 1615–1637, 2019, doi: 10.1007/s10231-019-00834-z.","chicago":"Winkler, Michael. “How Strong Singularities Can Be Regularized by Logistic Degradation in the Keller–Segel System?” Annali Di Matematica Pura Ed Applicata (1923 -) 198, no. 5 (2019): 1615–37. https://doi.org/10.1007/s10231-019-00834-z.","ama":"Winkler M. How strong singularities can be regularized by logistic degradation in the Keller–Segel system? Annali di Matematica Pura ed Applicata (1923 -). 2019;198(5):1615-1637. doi:10.1007/s10231-019-00834-z","apa":"Winkler, M. (2019). How strong singularities can be regularized by logistic degradation in the Keller–Segel system? Annali Di Matematica Pura Ed Applicata (1923 -), 198(5), 1615–1637. https://doi.org/10.1007/s10231-019-00834-z","short":"M. Winkler, Annali Di Matematica Pura Ed Applicata (1923 -) 198 (2019) 1615–1637.","mla":"Winkler, Michael. “How Strong Singularities Can Be Regularized by Logistic Degradation in the Keller–Segel System?” Annali Di Matematica Pura Ed Applicata (1923 -), vol. 198, no. 5, Springer Science and Business Media LLC, 2019, pp. 1615–37, doi:10.1007/s10231-019-00834-z.","bibtex":"@article{Winkler_2019, title={How strong singularities can be regularized by logistic degradation in the Keller–Segel system?}, volume={198}, DOI={10.1007/s10231-019-00834-z}, number={5}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2019}, pages={1615–1637} }"},"publication_identifier":{"issn":["0373-3114","1618-1891"]},"publication_status":"published","issue":"5","title":"How strong singularities can be regularized by logistic degradation in the Keller–Segel system?","doi":"10.1007/s10231-019-00834-z","date_updated":"2025-12-19T11:00:04Z","publisher":"Springer Science and Business Media LLC","volume":198,"date_created":"2025-12-19T10:59:58Z","author":[{"last_name":"Winkler","id":"31496","full_name":"Winkler, Michael","first_name":"Michael"}],"status":"public","publication":"Annali di Matematica Pura ed Applicata (1923 -)","type":"journal_article","language":[{"iso":"eng"}],"_id":"63364","user_id":"31496"},{"status":"public","publication":"Nonlinear Differential Equations and Applications NoDEA","type":"journal_article","language":[{"iso":"eng"}],"article_number":"48","user_id":"31496","_id":"63367","intvolume":" 26","citation":{"ieee":"M. Winkler, “Does repulsion-type directional preference in chemotactic migration continue to regularize Keller–Segel systems when coupled to the Navier–Stokes equations?,” Nonlinear Differential Equations and Applications NoDEA, vol. 26, no. 6, Art. no. 48, 2019, doi: 10.1007/s00030-019-0600-8.","chicago":"Winkler, Michael. “Does Repulsion-Type Directional Preference in Chemotactic Migration Continue to Regularize Keller–Segel Systems When Coupled to the Navier–Stokes Equations?” Nonlinear Differential Equations and Applications NoDEA 26, no. 6 (2019). https://doi.org/10.1007/s00030-019-0600-8.","ama":"Winkler M. Does repulsion-type directional preference in chemotactic migration continue to regularize Keller–Segel systems when coupled to the Navier–Stokes equations? Nonlinear Differential Equations and Applications NoDEA. 2019;26(6). doi:10.1007/s00030-019-0600-8","short":"M. Winkler, Nonlinear Differential Equations and Applications NoDEA 26 (2019).","mla":"Winkler, Michael. “Does Repulsion-Type Directional Preference in Chemotactic Migration Continue to Regularize Keller–Segel Systems When Coupled to the Navier–Stokes Equations?” Nonlinear Differential Equations and Applications NoDEA, vol. 26, no. 6, 48, Springer Science and Business Media LLC, 2019, doi:10.1007/s00030-019-0600-8.","bibtex":"@article{Winkler_2019, title={Does repulsion-type directional preference in chemotactic migration continue to regularize Keller–Segel systems when coupled to the Navier–Stokes equations?}, volume={26}, DOI={10.1007/s00030-019-0600-8}, number={648}, journal={Nonlinear Differential Equations and Applications NoDEA}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2019} }","apa":"Winkler, M. (2019). Does repulsion-type directional preference in chemotactic migration continue to regularize Keller–Segel systems when coupled to the Navier–Stokes equations? Nonlinear Differential Equations and Applications NoDEA, 26(6), Article 48. https://doi.org/10.1007/s00030-019-0600-8"},"year":"2019","issue":"6","publication_identifier":{"issn":["1021-9722","1420-9004"]},"publication_status":"published","doi":"10.1007/s00030-019-0600-8","title":"Does repulsion-type directional preference in chemotactic migration continue to regularize Keller–Segel systems when coupled to the Navier–Stokes equations?","volume":26,"author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-19T11:01:41Z","date_updated":"2025-12-19T11:01:47Z","publisher":"Springer Science and Business Media LLC"},{"user_id":"31496","_id":"63354","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","type":"journal_article","status":"public","volume":367,"date_created":"2025-12-19T10:52:55Z","author":[{"first_name":"Philippe","last_name":"Souplet","full_name":"Souplet, Philippe"},{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-19T10:53:03Z","doi":"10.1007/s00220-018-3238-1","title":"Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3","issue":"2","publication_identifier":{"issn":["0010-3616","1432-0916"]},"publication_status":"published","page":"665-681","intvolume":" 367","citation":{"apa":"Souplet, P., & Winkler, M. (2018). Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3. Communications in Mathematical Physics, 367(2), 665–681. https://doi.org/10.1007/s00220-018-3238-1","bibtex":"@article{Souplet_Winkler_2018, title={Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3}, volume={367}, DOI={10.1007/s00220-018-3238-1}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Souplet, Philippe and Winkler, Michael}, year={2018}, pages={665–681} }","short":"P. Souplet, M. Winkler, Communications in Mathematical Physics 367 (2018) 665–681.","mla":"Souplet, Philippe, and Michael Winkler. “Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3.” Communications in Mathematical Physics, vol. 367, no. 2, Springer Science and Business Media LLC, 2018, pp. 665–81, doi:10.1007/s00220-018-3238-1.","ama":"Souplet P, Winkler M. Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3. Communications in Mathematical Physics. 2018;367(2):665-681. doi:10.1007/s00220-018-3238-1","chicago":"Souplet, Philippe, and Michael Winkler. “Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3.” Communications in Mathematical Physics 367, no. 2 (2018): 665–81. https://doi.org/10.1007/s00220-018-3238-1.","ieee":"P. Souplet and M. Winkler, “Blow-up Profiles for the Parabolic–Elliptic Keller–Segel System in Dimensions $${n\\geq 3}$$ n ≥ 3,” Communications in Mathematical Physics, vol. 367, no. 2, pp. 665–681, 2018, doi: 10.1007/s00220-018-3238-1."},"year":"2018"},{"title":"How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases","doi":"10.1007/s00208-018-1722-8","date_updated":"2025-12-19T10:58:06Z","publisher":"Springer Science and Business Media LLC","date_created":"2025-12-19T10:57:59Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"volume":373,"year":"2018","citation":{"chicago":"Winkler, Michael. “How Unstable Is Spatial Homogeneity in Keller-Segel Systems? A New Critical Mass Phenomenon in Two- and Higher-Dimensional Parabolic-Elliptic Cases.” Mathematische Annalen 373, no. 3–4 (2018): 1237–82. https://doi.org/10.1007/s00208-018-1722-8.","ieee":"M. Winkler, “How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases,” Mathematische Annalen, vol. 373, no. 3–4, pp. 1237–1282, 2018, doi: 10.1007/s00208-018-1722-8.","ama":"Winkler M. How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Mathematische Annalen. 2018;373(3-4):1237-1282. doi:10.1007/s00208-018-1722-8","apa":"Winkler, M. (2018). How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases. Mathematische Annalen, 373(3–4), 1237–1282. https://doi.org/10.1007/s00208-018-1722-8","mla":"Winkler, Michael. “How Unstable Is Spatial Homogeneity in Keller-Segel Systems? A New Critical Mass Phenomenon in Two- and Higher-Dimensional Parabolic-Elliptic Cases.” Mathematische Annalen, vol. 373, no. 3–4, Springer Science and Business Media LLC, 2018, pp. 1237–82, doi:10.1007/s00208-018-1722-8.","short":"M. Winkler, Mathematische Annalen 373 (2018) 1237–1282.","bibtex":"@article{Winkler_2018, title={How unstable is spatial homogeneity in Keller-Segel systems? A new critical mass phenomenon in two- and higher-dimensional parabolic-elliptic cases}, volume={373}, DOI={10.1007/s00208-018-1722-8}, number={3–4}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2018}, pages={1237–1282} }"},"intvolume":" 373","page":"1237-1282","publication_status":"published","publication_identifier":{"issn":["0025-5831","1432-1807"]},"issue":"3-4","language":[{"iso":"eng"}],"_id":"63361","user_id":"31496","status":"public","type":"journal_article","publication":"Mathematische Annalen"},{"_id":"63365","user_id":"31496","language":[{"iso":"eng"}],"publication":"Journal of Differential Equations","type":"journal_article","status":"public","date_updated":"2025-12-19T11:00:31Z","publisher":"Elsevier BV","volume":266,"date_created":"2025-12-19T11:00:24Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"title":"Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities","doi":"10.1016/j.jde.2018.12.019","publication_identifier":{"issn":["0022-0396"]},"publication_status":"published","issue":"12","year":"2018","page":"8034-8066","intvolume":" 266","citation":{"bibtex":"@article{Winkler_2018, title={Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities}, volume={266}, DOI={10.1016/j.jde.2018.12.019}, number={12}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2018}, pages={8034–8066} }","short":"M. Winkler, Journal of Differential Equations 266 (2018) 8034–8066.","mla":"Winkler, Michael. “Global Classical Solvability and Generic Infinite-Time Blow-up in Quasilinear Keller–Segel Systems with Bounded Sensitivities.” Journal of Differential Equations, vol. 266, no. 12, Elsevier BV, 2018, pp. 8034–66, doi:10.1016/j.jde.2018.12.019.","apa":"Winkler, M. (2018). Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities. Journal of Differential Equations, 266(12), 8034–8066. https://doi.org/10.1016/j.jde.2018.12.019","ama":"Winkler M. Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities. Journal of Differential Equations. 2018;266(12):8034-8066. doi:10.1016/j.jde.2018.12.019","chicago":"Winkler, Michael. “Global Classical Solvability and Generic Infinite-Time Blow-up in Quasilinear Keller–Segel Systems with Bounded Sensitivities.” Journal of Differential Equations 266, no. 12 (2018): 8034–66. https://doi.org/10.1016/j.jde.2018.12.019.","ieee":"M. Winkler, “Global classical solvability and generic infinite-time blow-up in quasilinear Keller–Segel systems with bounded sensitivities,” Journal of Differential Equations, vol. 266, no. 12, pp. 8034–8066, 2018, doi: 10.1016/j.jde.2018.12.019."}},{"language":[{"iso":"eng"}],"_id":"63360","user_id":"31496","status":"public","type":"journal_article","publication":"Journal of Functional Analysis","title":"A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization","doi":"10.1016/j.jfa.2018.12.009","date_updated":"2025-12-19T10:57:36Z","publisher":"Elsevier BV","date_created":"2025-12-19T10:57:28Z","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"volume":276,"year":"2018","citation":{"bibtex":"@article{Winkler_2018, title={A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization}, volume={276}, DOI={10.1016/j.jfa.2018.12.009}, number={5}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2018}, pages={1339–1401} }","mla":"Winkler, Michael. “A Three-Dimensional Keller–Segel–Navier–Stokes System with Logistic Source: Global Weak Solutions and Asymptotic Stabilization.” Journal of Functional Analysis, vol. 276, no. 5, Elsevier BV, 2018, pp. 1339–401, doi:10.1016/j.jfa.2018.12.009.","short":"M. Winkler, Journal of Functional Analysis 276 (2018) 1339–1401.","apa":"Winkler, M. (2018). A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization. Journal of Functional Analysis, 276(5), 1339–1401. https://doi.org/10.1016/j.jfa.2018.12.009","ama":"Winkler M. A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization. Journal of Functional Analysis. 2018;276(5):1339-1401. doi:10.1016/j.jfa.2018.12.009","ieee":"M. Winkler, “A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization,” Journal of Functional Analysis, vol. 276, no. 5, pp. 1339–1401, 2018, doi: 10.1016/j.jfa.2018.12.009.","chicago":"Winkler, Michael. “A Three-Dimensional Keller–Segel–Navier–Stokes System with Logistic Source: Global Weak Solutions and Asymptotic Stabilization.” Journal of Functional Analysis 276, no. 5 (2018): 1339–1401. https://doi.org/10.1016/j.jfa.2018.12.009."},"page":"1339-1401","intvolume":" 276","publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"issue":"5"},{"issue":"5","publication_identifier":{"issn":["0308-2105","1473-7124"]},"publication_status":"published","page":"939-955","intvolume":" 148","citation":{"bibtex":"@article{Cao_Winkler_2018, title={Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains}, volume={148}, DOI={10.1017/s0308210518000057}, number={5}, journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics}, publisher={Cambridge University Press (CUP)}, author={Cao, Xinru and Winkler, Michael}, year={2018}, pages={939–955} }","short":"X. Cao, M. Winkler, Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148 (2018) 939–955.","mla":"Cao, Xinru, and Michael Winkler. “Sharp Decay Estimates in a Bioconvection Model with Quadratic Degradation in Bounded Domains.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 148, no. 5, Cambridge University Press (CUP), 2018, pp. 939–55, doi:10.1017/s0308210518000057.","apa":"Cao, X., & Winkler, M. (2018). Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 148(5), 939–955. https://doi.org/10.1017/s0308210518000057","ama":"Cao X, Winkler M. Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2018;148(5):939-955. doi:10.1017/s0308210518000057","ieee":"X. Cao and M. Winkler, “Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 148, no. 5, pp. 939–955, 2018, doi: 10.1017/s0308210518000057.","chicago":"Cao, Xinru, and Michael Winkler. “Sharp Decay Estimates in a Bioconvection Model with Quadratic Degradation in Bounded Domains.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 5 (2018): 939–55. https://doi.org/10.1017/s0308210518000057."},"year":"2018","volume":148,"date_created":"2025-12-19T11:02:55Z","author":[{"last_name":"Cao","full_name":"Cao, Xinru","first_name":"Xinru"},{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_updated":"2025-12-19T11:03:03Z","publisher":"Cambridge University Press (CUP)","doi":"10.1017/s0308210518000057","title":"Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains","publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"The paper studies large time behaviour of solutions to the Keller–Segel system with quadratic degradation in a liquid environment, as given byunder Neumann boundary conditions in a bounded domain Ω ⊂ ℝn, where n ≥ 1 is arbitrary. It is shown that whenever U : Ω × (0,∞) → ℝn is a bounded and sufficiently regular solenoidal vector field any non-trivial global bounded solution of (⋆) approaches the trivial equilibrium at a rate that, with respect to the norm in either of the spaces L1(Ω) and L∞(Ω), can be controlled from above and below by appropriate multiples of 1/(t + 1). This underlines that, even up to this quantitative level of accuracy, the large time behaviour in (⋆) is essentially independent not only of the particular fluid flow, but also of any effect originating from chemotactic cross-diffusion. The latter is in contrast to the corresponding Cauchy problem, for which known results show that in the n = 2 case the presence of chemotaxis can significantly enhance biomixing by reducing the respective spatial L1 norms of solutions."}],"user_id":"31496","_id":"63369","language":[{"iso":"eng"}]},{"page":"1-17","intvolume":" 163","citation":{"mla":"Winkler, Michael. “Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity.” Acta Applicandae Mathematicae, vol. 163, no. 1, Springer Science and Business Media LLC, 2018, pp. 1–17, doi:10.1007/s10440-018-0211-0.","bibtex":"@article{Winkler_2018, title={Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity}, volume={163}, DOI={10.1007/s10440-018-0211-0}, number={1}, journal={Acta Applicandae Mathematicae}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2018}, pages={1–17} }","short":"M. Winkler, Acta Applicandae Mathematicae 163 (2018) 1–17.","apa":"Winkler, M. (2018). Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity. Acta Applicandae Mathematicae, 163(1), 1–17. https://doi.org/10.1007/s10440-018-0211-0","chicago":"Winkler, Michael. “Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity.” Acta Applicandae Mathematicae 163, no. 1 (2018): 1–17. https://doi.org/10.1007/s10440-018-0211-0.","ieee":"M. Winkler, “Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity,” Acta Applicandae Mathematicae, vol. 163, no. 1, pp. 1–17, 2018, doi: 10.1007/s10440-018-0211-0.","ama":"Winkler M. Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity. Acta Applicandae Mathematicae. 2018;163(1):1-17. doi:10.1007/s10440-018-0211-0"},"year":"2018","issue":"1","publication_identifier":{"issn":["0167-8019","1572-9036"]},"publication_status":"published","doi":"10.1007/s10440-018-0211-0","title":"Boundedness in a Chemotaxis-May-Nowak Model for Virus Dynamics with Mildly Saturated Chemotactic Sensitivity","volume":163,"author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-19T11:02:13Z","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-19T11:02:21Z","status":"public","publication":"Acta Applicandae Mathematicae","type":"journal_article","language":[{"iso":"eng"}],"user_id":"31496","_id":"63368"},{"type":"journal_article","publication":"Nonlinearity","status":"public","user_id":"31496","_id":"63370","language":[{"iso":"eng"}],"issue":"4","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"citation":{"bibtex":"@article{Espejo_Winkler_2018, title={Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization}, volume={31}, DOI={10.1088/1361-6544/aa9d5f}, number={4}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Espejo, Elio and Winkler, Michael}, year={2018}, pages={1227–1259} }","short":"E. Espejo, M. Winkler, Nonlinearity 31 (2018) 1227–1259.","mla":"Espejo, Elio, and Michael Winkler. “Global Classical Solvability and Stabilization in a Two-Dimensional Chemotaxis-Navier–Stokes System Modeling Coral Fertilization.” Nonlinearity, vol. 31, no. 4, IOP Publishing, 2018, pp. 1227–59, doi:10.1088/1361-6544/aa9d5f.","apa":"Espejo, E., & Winkler, M. (2018). Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization. Nonlinearity, 31(4), 1227–1259. https://doi.org/10.1088/1361-6544/aa9d5f","chicago":"Espejo, Elio, and Michael Winkler. “Global Classical Solvability and Stabilization in a Two-Dimensional Chemotaxis-Navier–Stokes System Modeling Coral Fertilization.” Nonlinearity 31, no. 4 (2018): 1227–59. https://doi.org/10.1088/1361-6544/aa9d5f.","ieee":"E. Espejo and M. Winkler, “Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization,” Nonlinearity, vol. 31, no. 4, pp. 1227–1259, 2018, doi: 10.1088/1361-6544/aa9d5f.","ama":"Espejo E, Winkler M. Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization. Nonlinearity. 2018;31(4):1227-1259. doi:10.1088/1361-6544/aa9d5f"},"intvolume":" 31","page":"1227-1259","year":"2018","author":[{"full_name":"Espejo, Elio","last_name":"Espejo","first_name":"Elio"},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-19T11:03:26Z","volume":31,"publisher":"IOP Publishing","date_updated":"2025-12-19T11:03:32Z","doi":"10.1088/1361-6544/aa9d5f","title":"Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier–Stokes system modeling coral fertilization"},{"publication_identifier":{"issn":["0044-2275","1420-9039"]},"publication_status":"published","issue":"2","year":"2018","intvolume":" 69","citation":{"apa":"Winkler, M. (2018). Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation. Zeitschrift Für Angewandte Mathematik Und Physik, 69(2), Article 40. https://doi.org/10.1007/s00033-018-0935-8","mla":"Winkler, Michael. “Finite-Time Blow-up in Low-Dimensional Keller–Segel Systems with Logistic-Type Superlinear Degradation.” Zeitschrift Für Angewandte Mathematik Und Physik, vol. 69, no. 2, 40, Springer Science and Business Media LLC, 2018, doi:10.1007/s00033-018-0935-8.","short":"M. Winkler, Zeitschrift Für Angewandte Mathematik Und Physik 69 (2018).","bibtex":"@article{Winkler_2018, title={Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation}, volume={69}, DOI={10.1007/s00033-018-0935-8}, number={240}, journal={Zeitschrift für angewandte Mathematik und Physik}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2018} }","ieee":"M. Winkler, “Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation,” Zeitschrift für angewandte Mathematik und Physik, vol. 69, no. 2, Art. no. 40, 2018, doi: 10.1007/s00033-018-0935-8.","chicago":"Winkler, Michael. “Finite-Time Blow-up in Low-Dimensional Keller–Segel Systems with Logistic-Type Superlinear Degradation.” Zeitschrift Für Angewandte Mathematik Und Physik 69, no. 2 (2018). https://doi.org/10.1007/s00033-018-0935-8.","ama":"Winkler M. Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation. Zeitschrift für angewandte Mathematik und Physik. 2018;69(2). doi:10.1007/s00033-018-0935-8"},"date_updated":"2025-12-19T11:07:05Z","publisher":"Springer Science and Business Media LLC","volume":69,"author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"}],"date_created":"2025-12-19T11:06:58Z","title":"Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation","doi":"10.1007/s00033-018-0935-8","publication":"Zeitschrift für angewandte Mathematik und Physik","type":"journal_article","status":"public","_id":"63377","user_id":"31496","article_number":"40","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"_id":"63375","user_id":"31496","status":"public","publication":"Journal of Mathematical Fluid Mechanics","type":"journal_article","title":"Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity?","doi":"10.1007/s00021-018-0395-0","publisher":"Springer Science and Business Media LLC","date_updated":"2025-12-19T11:06:09Z","volume":20,"author":[{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2025-12-19T11:06:02Z","year":"2018","intvolume":" 20","page":"1889-1909","citation":{"short":"M. Winkler, Journal of Mathematical Fluid Mechanics 20 (2018) 1889–1909.","bibtex":"@article{Winkler_2018, title={Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity?}, volume={20}, DOI={10.1007/s00021-018-0395-0}, number={4}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2018}, pages={1889–1909} }","mla":"Winkler, Michael. “Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity?” Journal of Mathematical Fluid Mechanics, vol. 20, no. 4, Springer Science and Business Media LLC, 2018, pp. 1889–909, doi:10.1007/s00021-018-0395-0.","apa":"Winkler, M. (2018). Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity? Journal of Mathematical Fluid Mechanics, 20(4), 1889–1909. https://doi.org/10.1007/s00021-018-0395-0","ama":"Winkler M. Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity? Journal of Mathematical Fluid Mechanics. 2018;20(4):1889-1909. doi:10.1007/s00021-018-0395-0","chicago":"Winkler, Michael. “Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity?” Journal of Mathematical Fluid Mechanics 20, no. 4 (2018): 1889–1909. https://doi.org/10.1007/s00021-018-0395-0.","ieee":"M. Winkler, “Does Fluid Interaction Affect Regularity in the Three-Dimensional Keller–Segel System with Saturated Sensitivity?,” Journal of Mathematical Fluid Mechanics, vol. 20, no. 4, pp. 1889–1909, 2018, doi: 10.1007/s00021-018-0395-0."},"publication_identifier":{"issn":["1422-6928","1422-6952"]},"publication_status":"published","issue":"4"},{"status":"public","publication":"Journal of Evolution Equations","type":"journal_article","language":[{"iso":"eng"}],"_id":"63381","user_id":"31496","year":"2018","intvolume":" 18","page":"1267-1289","citation":{"ieee":"M. Winkler, “Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components,” Journal of Evolution Equations, vol. 18, no. 3, pp. 1267–1289, 2018, doi: 10.1007/s00028-018-0440-8.","chicago":"Winkler, Michael. “Global Mass-Preserving Solutions in a Two-Dimensional Chemotaxis-Stokes System with Rotational Flux Components.” Journal of Evolution Equations 18, no. 3 (2018): 1267–89. https://doi.org/10.1007/s00028-018-0440-8.","ama":"Winkler M. Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Journal of Evolution Equations. 2018;18(3):1267-1289. doi:10.1007/s00028-018-0440-8","apa":"Winkler, M. (2018). Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components. Journal of Evolution Equations, 18(3), 1267–1289. https://doi.org/10.1007/s00028-018-0440-8","mla":"Winkler, Michael. “Global Mass-Preserving Solutions in a Two-Dimensional Chemotaxis-Stokes System with Rotational Flux Components.” Journal of Evolution Equations, vol. 18, no. 3, Springer Science and Business Media LLC, 2018, pp. 1267–89, doi:10.1007/s00028-018-0440-8.","bibtex":"@article{Winkler_2018, title={Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components}, volume={18}, DOI={10.1007/s00028-018-0440-8}, number={3}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2018}, pages={1267–1289} }","short":"M. Winkler, Journal of Evolution Equations 18 (2018) 1267–1289."},"publication_identifier":{"issn":["1424-3199","1424-3202"]},"publication_status":"published","issue":"3","title":"Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components","doi":"10.1007/s00028-018-0440-8","date_updated":"2025-12-19T11:08:50Z","publisher":"Springer Science and Business Media LLC","volume":18,"date_created":"2025-12-19T11:08:43Z","author":[{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}]},{"date_created":"2025-12-19T11:08:16Z","author":[{"last_name":"Winkler","full_name":"Winkler, Michael","id":"31496","first_name":"Michael"}],"volume":264,"publisher":"Elsevier BV","date_updated":"2025-12-19T11:08:22Z","doi":"10.1016/j.jde.2018.01.027","title":"Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement","issue":"10","publication_status":"published","publication_identifier":{"issn":["0022-0396"]},"citation":{"ieee":"M. Winkler, “Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement,” Journal of Differential Equations, vol. 264, no. 10, pp. 6109–6151, 2018, doi: 10.1016/j.jde.2018.01.027.","chicago":"Winkler, Michael. “Global Existence and Stabilization in a Degenerate Chemotaxis-Stokes System with Mildly Strong Diffusion Enhancement.” Journal of Differential Equations 264, no. 10 (2018): 6109–51. https://doi.org/10.1016/j.jde.2018.01.027.","ama":"Winkler M. Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Journal of Differential Equations. 2018;264(10):6109-6151. doi:10.1016/j.jde.2018.01.027","short":"M. Winkler, Journal of Differential Equations 264 (2018) 6109–6151.","mla":"Winkler, Michael. “Global Existence and Stabilization in a Degenerate Chemotaxis-Stokes System with Mildly Strong Diffusion Enhancement.” Journal of Differential Equations, vol. 264, no. 10, Elsevier BV, 2018, pp. 6109–51, doi:10.1016/j.jde.2018.01.027.","bibtex":"@article{Winkler_2018, title={Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement}, volume={264}, DOI={10.1016/j.jde.2018.01.027}, number={10}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Winkler, Michael}, year={2018}, pages={6109–6151} }","apa":"Winkler, M. (2018). Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement. Journal of Differential Equations, 264(10), 6109–6151. https://doi.org/10.1016/j.jde.2018.01.027"},"page":"6109-6151","intvolume":" 264","year":"2018","user_id":"31496","_id":"63380","language":[{"iso":"eng"}],"type":"journal_article","publication":"Journal of Differential Equations","status":"public"},{"title":"A critical blow-up exponent in a chemotaxis system with nonlinear signal production","doi":"10.1088/1361-6544/aaaa0e","publisher":"IOP Publishing","date_updated":"2025-12-19T11:06:40Z","author":[{"full_name":"Winkler, Michael","id":"31496","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-19T11:06:33Z","volume":31,"year":"2018","citation":{"ieee":"M. Winkler, “A critical blow-up exponent in a chemotaxis system with nonlinear signal production,” Nonlinearity, vol. 31, no. 5, pp. 2031–2056, 2018, doi: 10.1088/1361-6544/aaaa0e.","chicago":"Winkler, Michael. “A Critical Blow-up Exponent in a Chemotaxis System with Nonlinear Signal Production.” Nonlinearity 31, no. 5 (2018): 2031–56. https://doi.org/10.1088/1361-6544/aaaa0e.","ama":"Winkler M. A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Nonlinearity. 2018;31(5):2031-2056. doi:10.1088/1361-6544/aaaa0e","apa":"Winkler, M. (2018). A critical blow-up exponent in a chemotaxis system with nonlinear signal production. Nonlinearity, 31(5), 2031–2056. https://doi.org/10.1088/1361-6544/aaaa0e","short":"M. Winkler, Nonlinearity 31 (2018) 2031–2056.","mla":"Winkler, Michael. “A Critical Blow-up Exponent in a Chemotaxis System with Nonlinear Signal Production.” Nonlinearity, vol. 31, no. 5, IOP Publishing, 2018, pp. 2031–56, doi:10.1088/1361-6544/aaaa0e.","bibtex":"@article{Winkler_2018, title={A critical blow-up exponent in a chemotaxis system with nonlinear signal production}, volume={31}, DOI={10.1088/1361-6544/aaaa0e}, number={5}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Winkler, Michael}, year={2018}, pages={2031–2056} }"},"page":"2031-2056","intvolume":" 31","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"issue":"5","language":[{"iso":"eng"}],"_id":"63376","user_id":"31496","status":"public","type":"journal_article","publication":"Nonlinearity"},{"language":[{"iso":"eng"}],"user_id":"31496","_id":"63382","status":"public","type":"journal_article","publication":"Nonlinear Analysis","doi":"10.1016/j.na.2018.01.002","title":"Stabilization in the logarithmic Keller–Segel system","date_created":"2025-12-19T11:09:11Z","author":[{"first_name":"Michael","full_name":"Winkler, Michael","id":"31496","last_name":"Winkler"},{"last_name":"Yokota","full_name":"Yokota, Tomomi","first_name":"Tomomi"}],"volume":170,"publisher":"Elsevier BV","date_updated":"2025-12-19T11:09:19Z","citation":{"ama":"Winkler M, Yokota T. Stabilization in the logarithmic Keller–Segel system. Nonlinear Analysis. 2018;170:123-141. doi:10.1016/j.na.2018.01.002","chicago":"Winkler, Michael, and Tomomi Yokota. “Stabilization in the Logarithmic Keller–Segel System.” Nonlinear Analysis 170 (2018): 123–41. https://doi.org/10.1016/j.na.2018.01.002.","ieee":"M. Winkler and T. Yokota, “Stabilization in the logarithmic Keller–Segel system,” Nonlinear Analysis, vol. 170, pp. 123–141, 2018, doi: 10.1016/j.na.2018.01.002.","mla":"Winkler, Michael, and Tomomi Yokota. “Stabilization in the Logarithmic Keller–Segel System.” Nonlinear Analysis, vol. 170, Elsevier BV, 2018, pp. 123–41, doi:10.1016/j.na.2018.01.002.","short":"M. Winkler, T. Yokota, Nonlinear Analysis 170 (2018) 123–141.","bibtex":"@article{Winkler_Yokota_2018, title={Stabilization in the logarithmic Keller–Segel system}, volume={170}, DOI={10.1016/j.na.2018.01.002}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Winkler, Michael and Yokota, Tomomi}, year={2018}, pages={123–141} }","apa":"Winkler, M., & Yokota, T. (2018). Stabilization in the logarithmic Keller–Segel system. Nonlinear Analysis, 170, 123–141. https://doi.org/10.1016/j.na.2018.01.002"},"intvolume":" 170","page":"123-141","year":"2018","publication_status":"published","publication_identifier":{"issn":["0362-546X"]}},{"publisher":"Cambridge University Press (CUP)","date_updated":"2025-12-19T11:03:57Z","volume":29,"author":[{"full_name":"HILLEN, T.","last_name":"HILLEN","first_name":"T."},{"last_name":"PAINTER","full_name":"PAINTER, K. J.","first_name":"K. J."},{"id":"31496","full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2025-12-19T11:03:50Z","title":"Global solvability and explicit bounds for non-local adhesion models","doi":"10.1017/s0956792517000328","publication_identifier":{"issn":["0956-7925","1469-4425"]},"publication_status":"published","issue":"4","year":"2017","intvolume":" 29","page":"645-684","citation":{"apa":"HILLEN, T., PAINTER, K. J., & Winkler, M. (2017). Global solvability and explicit bounds for non-local adhesion models. European Journal of Applied Mathematics, 29(4), 645–684. https://doi.org/10.1017/s0956792517000328","mla":"HILLEN, T., et al. “Global Solvability and Explicit Bounds for Non-Local Adhesion Models.” European Journal of Applied Mathematics, vol. 29, no. 4, Cambridge University Press (CUP), 2017, pp. 645–84, doi:10.1017/s0956792517000328.","short":"T. HILLEN, K.J. PAINTER, M. Winkler, European Journal of Applied Mathematics 29 (2017) 645–684.","bibtex":"@article{HILLEN_PAINTER_Winkler_2017, title={Global solvability and explicit bounds for non-local adhesion models}, volume={29}, DOI={10.1017/s0956792517000328}, number={4}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={HILLEN, T. and PAINTER, K. J. and Winkler, Michael}, year={2017}, pages={645–684} }","chicago":"HILLEN, T., K. J. PAINTER, and Michael Winkler. “Global Solvability and Explicit Bounds for Non-Local Adhesion Models.” European Journal of Applied Mathematics 29, no. 4 (2017): 645–84. https://doi.org/10.1017/s0956792517000328.","ieee":"T. HILLEN, K. J. PAINTER, and M. Winkler, “Global solvability and explicit bounds for non-local adhesion models,” European Journal of Applied Mathematics, vol. 29, no. 4, pp. 645–684, 2017, doi: 10.1017/s0956792517000328.","ama":"HILLEN T, PAINTER KJ, Winkler M. Global solvability and explicit bounds for non-local adhesion models. European Journal of Applied Mathematics. 2017;29(4):645-684. doi:10.1017/s0956792517000328"},"_id":"63371","user_id":"31496","language":[{"iso":"eng"}],"publication":"European Journal of Applied Mathematics","type":"journal_article","abstract":[{"text":"Adhesion between cells and other cells (cell–cell adhesion) or other tissue components (cell–matrix adhesion) is an intrinsically non-local phenomenon. Consequently, a number of recently developed mathematical models for cell adhesion have taken the form of non-local partial differential equations, where the non-local term arises inside a spatial derivative. The mathematical properties of such a non-local gradient term are not yet well understood. Here we use sophisticated estimation techniques to show local and global existence of classical solutions for such examples of adhesion-type models, and we provide a uniform upper bound for the solutions. Further, we discuss the significance of these results to applications in cell sorting and in cancer invasion and support the theoretical results through numerical simulations.","lang":"eng"}],"status":"public"}]