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Global Very Weak Solutions to a Chemotaxis-Fluid System with Nonlinear Diffusion. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(4):4087-4116. doi:<a href=\"https://doi.org/10.1137/17m1159488\">10.1137/17m1159488</a>"},"intvolume":"        50","page":"4087-4116","year":"2018","issue":"4","publication_status":"published","publication_identifier":{"issn":["0036-1410","1095-7154"]},"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"user_id":"23686","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"_id":"34664","status":"public","type":"journal_article","publication":"SIAM Journal on Mathematical Analysis"},{"publication_status":"published","publication_identifier":{"issn":["0022-0396"]},"citation":{"chicago":"Black, Tobias. “Eventual Smoothness of Generalized Solutions to a Singular Chemotaxis-Stokes System in 2D.” <i>Journal of Differential Equations</i> 265, no. 5 (2018): 2296–2339. <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">https://doi.org/10.1016/j.jde.2018.04.035</a>.","ieee":"T. 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Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D. <i>Journal of Differential Equations</i>, <i>265</i>(5), 2296–2339. <a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">https://doi.org/10.1016/j.jde.2018.04.035</a>","bibtex":"@article{Black_2018, title={Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D}, volume={265}, DOI={<a href=\"https://doi.org/10.1016/j.jde.2018.04.035\">10.1016/j.jde.2018.04.035</a>}, number={5}, journal={Journal of Differential Equations}, publisher={Elsevier BV}, author={Black, Tobias}, year={2018}, pages={2296–2339} }","short":"T. 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Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions. <i>Nonlinear Analysis</i>, <i>180</i>, 129–153. <a href=\"https://doi.org/10.1016/j.na.2018.10.003\">https://doi.org/10.1016/j.na.2018.10.003</a>","bibtex":"@article{Black_2018, title={Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions}, volume={180}, DOI={<a href=\"https://doi.org/10.1016/j.na.2018.10.003\">10.1016/j.na.2018.10.003</a>}, journal={Nonlinear Analysis}, publisher={Elsevier BV}, author={Black, Tobias}, year={2018}, pages={129–153} }","short":"T. 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Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i>. 2017;22(4):1253-1272. doi:<a href=\"https://doi.org/10.3934/dcdsb.2017061\">10.3934/dcdsb.2017061</a>","chicago":"Black, Tobias. “Global Existence and Asymptotic Stability in a Competitive Two-Species Chemotaxis System with Two Signals.” <i>Discrete &#38;amp; Continuous Dynamical Systems - B</i> 22, no. 4 (2017): 1253–72. <a href=\"https://doi.org/10.3934/dcdsb.2017061\">https://doi.org/10.3934/dcdsb.2017061</a>.","ieee":"T. 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Singular sensitivity in a Keller–Segel-fluid system. <i>Journal of Evolution Equations</i>, <i>18</i>(2), 561–581. <a href=\"https://doi.org/10.1007/s00028-017-0411-5\">https://doi.org/10.1007/s00028-017-0411-5</a>","mla":"Black, Tobias, et al. “Singular Sensitivity in a Keller–Segel-Fluid System.” <i>Journal of Evolution Equations</i>, vol. 18, no. 2, Springer Science and Business Media LLC, 2017, pp. 561–81, doi:<a href=\"https://doi.org/10.1007/s00028-017-0411-5\">10.1007/s00028-017-0411-5</a>.","short":"T. Black, J. Lankeit, M. Mizukami, Journal of Evolution Equations 18 (2017) 561–581.","bibtex":"@article{Black_Lankeit_Mizukami_2017, title={Singular sensitivity in a Keller–Segel-fluid system}, volume={18}, DOI={<a href=\"https://doi.org/10.1007/s00028-017-0411-5\">10.1007/s00028-017-0411-5</a>}, number={2}, journal={Journal of Evolution Equations}, publisher={Springer Science and Business Media LLC}, author={Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}, year={2017}, pages={561–581} }"},"publication_identifier":{"issn":["1424-3199","1424-3202"]},"publication_status":"published","_id":"34665","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"user_id":"23686","status":"public","type":"journal_article"},{"type":"journal_article","publication":"IMA Journal of Applied Mathematics","status":"public","user_id":"23686","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"_id":"34660","language":[{"iso":"eng"}],"keyword":["Applied Mathematics"],"issue":"5","publication_status":"published","publication_identifier":{"issn":["0272-4960","1464-3634"]},"citation":{"apa":"Black, T., Lankeit, J., &#38; Mizukami, M. (2016). On the weakly competitive case in a two-species chemotaxis model. <i>IMA Journal of Applied Mathematics</i>, <i>81</i>(5), 860–876. <a href=\"https://doi.org/10.1093/imamat/hxw036\">https://doi.org/10.1093/imamat/hxw036</a>","mla":"Black, Tobias, et al. “On the Weakly Competitive Case in a Two-Species Chemotaxis Model.” <i>IMA Journal of Applied Mathematics</i>, vol. 81, no. 5, Oxford University Press (OUP), 2016, pp. 860–76, doi:<a href=\"https://doi.org/10.1093/imamat/hxw036\">10.1093/imamat/hxw036</a>.","bibtex":"@article{Black_Lankeit_Mizukami_2016, title={On the weakly competitive case in a two-species chemotaxis model}, volume={81}, DOI={<a href=\"https://doi.org/10.1093/imamat/hxw036\">10.1093/imamat/hxw036</a>}, number={5}, journal={IMA Journal of Applied Mathematics}, publisher={Oxford University Press (OUP)}, author={Black, Tobias and Lankeit, Johannes and Mizukami, Masaaki}, year={2016}, pages={860–876} }","short":"T. Black, J. Lankeit, M. Mizukami, IMA Journal of Applied Mathematics 81 (2016) 860–876.","ama":"Black T, Lankeit J, Mizukami M. On the weakly competitive case in a two-species chemotaxis model. <i>IMA Journal of Applied Mathematics</i>. 2016;81(5):860-876. doi:<a href=\"https://doi.org/10.1093/imamat/hxw036\">10.1093/imamat/hxw036</a>","ieee":"T. Black, J. Lankeit, and M. Mizukami, “On the weakly competitive case in a two-species chemotaxis model,” <i>IMA Journal of Applied Mathematics</i>, vol. 81, no. 5, pp. 860–876, 2016, doi: <a href=\"https://doi.org/10.1093/imamat/hxw036\">10.1093/imamat/hxw036</a>.","chicago":"Black, Tobias, Johannes Lankeit, and Masaaki Mizukami. “On the Weakly Competitive Case in a Two-Species Chemotaxis Model.” <i>IMA Journal of Applied Mathematics</i> 81, no. 5 (2016): 860–76. <a href=\"https://doi.org/10.1093/imamat/hxw036\">https://doi.org/10.1093/imamat/hxw036</a>."},"intvolume":"        81","page":"860-876","year":"2016","date_created":"2022-12-21T09:46:18Z","author":[{"orcid":"0000-0001-9963-0800","last_name":"Black","full_name":"Black, Tobias","id":"23686","first_name":"Tobias"},{"first_name":"Johannes","full_name":"Lankeit, Johannes","last_name":"Lankeit"},{"full_name":"Mizukami, Masaaki","last_name":"Mizukami","first_name":"Masaaki"}],"volume":81,"publisher":"Oxford University Press (OUP)","date_updated":"2022-12-21T10:05:33Z","doi":"10.1093/imamat/hxw036","title":"On the weakly competitive case in a two-species chemotaxis model"},{"keyword":["Applied Mathematics","Analysis"],"language":[{"iso":"eng"}],"publication":"Journal of Mathematical Analysis and Applications","publisher":"Elsevier BV","date_created":"2022-12-21T09:46:40Z","title":"Boundedness in a Keller–Segel system with external signal production","issue":"1","year":"2016","_id":"34662","user_id":"23686","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"type":"journal_article","status":"public","date_updated":"2022-12-21T10:05:39Z","author":[{"first_name":"Tobias","full_name":"Black, Tobias","id":"23686","orcid":"0000-0001-9963-0800","last_name":"Black"}],"volume":446,"doi":"10.1016/j.jmaa.2016.08.049","publication_status":"published","publication_identifier":{"issn":["0022-247X"]},"citation":{"ama":"Black T. Boundedness in a Keller–Segel system with external signal production. <i>Journal of Mathematical Analysis and Applications</i>. 2016;446(1):436-455. doi:<a href=\"https://doi.org/10.1016/j.jmaa.2016.08.049\">10.1016/j.jmaa.2016.08.049</a>","chicago":"Black, Tobias. “Boundedness in a Keller–Segel System with External Signal Production.” <i>Journal of Mathematical Analysis and Applications</i> 446, no. 1 (2016): 436–55. <a href=\"https://doi.org/10.1016/j.jmaa.2016.08.049\">https://doi.org/10.1016/j.jmaa.2016.08.049</a>.","ieee":"T. Black, “Boundedness in a Keller–Segel system with external signal production,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 446, no. 1, pp. 436–455, 2016, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2016.08.049\">10.1016/j.jmaa.2016.08.049</a>.","apa":"Black, T. (2016). Boundedness in a Keller–Segel system with external signal production. <i>Journal of Mathematical Analysis and Applications</i>, <i>446</i>(1), 436–455. <a href=\"https://doi.org/10.1016/j.jmaa.2016.08.049\">https://doi.org/10.1016/j.jmaa.2016.08.049</a>","short":"T. Black, Journal of Mathematical Analysis and Applications 446 (2016) 436–455.","bibtex":"@article{Black_2016, title={Boundedness in a Keller–Segel system with external signal production}, volume={446}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2016.08.049\">10.1016/j.jmaa.2016.08.049</a>}, number={1}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Black, Tobias}, year={2016}, pages={436–455} }","mla":"Black, Tobias. “Boundedness in a Keller–Segel System with External Signal Production.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 446, no. 1, Elsevier BV, 2016, pp. 436–55, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2016.08.049\">10.1016/j.jmaa.2016.08.049</a>."},"page":"436-455","intvolume":"       446"},{"status":"public","type":"journal_article","publication":"Nonlinearity","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Physics and Astronomy","Mathematical Physics","Statistical and Nonlinear Physics"],"user_id":"23686","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"_id":"34659","citation":{"apa":"Black, T. (2016). Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant. <i>Nonlinearity</i>, <i>29</i>(6), 1865–1886. <a href=\"https://doi.org/10.1088/0951-7715/29/6/1865\">https://doi.org/10.1088/0951-7715/29/6/1865</a>","bibtex":"@article{Black_2016, title={Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant}, volume={29}, DOI={<a href=\"https://doi.org/10.1088/0951-7715/29/6/1865\">10.1088/0951-7715/29/6/1865</a>}, number={6}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Black, Tobias}, year={2016}, pages={1865–1886} }","short":"T. Black, Nonlinearity 29 (2016) 1865–1886.","mla":"Black, Tobias. “Blow-up of Weak Solutions to a Chemotaxis System under Influence of an External Chemoattractant.” <i>Nonlinearity</i>, vol. 29, no. 6, IOP Publishing, 2016, pp. 1865–86, doi:<a href=\"https://doi.org/10.1088/0951-7715/29/6/1865\">10.1088/0951-7715/29/6/1865</a>.","ama":"Black T. Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant. <i>Nonlinearity</i>. 2016;29(6):1865-1886. doi:<a href=\"https://doi.org/10.1088/0951-7715/29/6/1865\">10.1088/0951-7715/29/6/1865</a>","chicago":"Black, Tobias. “Blow-up of Weak Solutions to a Chemotaxis System under Influence of an External Chemoattractant.” <i>Nonlinearity</i> 29, no. 6 (2016): 1865–86. <a href=\"https://doi.org/10.1088/0951-7715/29/6/1865\">https://doi.org/10.1088/0951-7715/29/6/1865</a>.","ieee":"T. Black, “Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant,” <i>Nonlinearity</i>, vol. 29, no. 6, pp. 1865–1886, 2016, doi: <a href=\"https://doi.org/10.1088/0951-7715/29/6/1865\">10.1088/0951-7715/29/6/1865</a>."},"page":"1865-1886","intvolume":"        29","year":"2016","issue":"6","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"doi":"10.1088/0951-7715/29/6/1865","title":"Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant","author":[{"id":"23686","full_name":"Black, Tobias","orcid":"0000-0001-9963-0800","last_name":"Black","first_name":"Tobias"}],"date_created":"2022-12-21T09:46:00Z","volume":29,"date_updated":"2022-12-21T10:05:45Z","publisher":"IOP Publishing"},{"publication":"Nonlinear Analysis: Real World Applications","type":"journal_article","status":"public","department":[{"_id":"34"},{"_id":"10"},{"_id":"90"}],"user_id":"23686","_id":"34661","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","General Economics","Econometrics and Finance","General Engineering","General Medicine","Analysis"],"publication_identifier":{"issn":["1468-1218"]},"publication_status":"published","page":"593-609","intvolume":"        31","citation":{"apa":"Black, T. (2016). Sublinear signal production in a two-dimensional Keller–Segel–Stokes system. <i>Nonlinear Analysis: Real World Applications</i>, <i>31</i>, 593–609. <a href=\"https://doi.org/10.1016/j.nonrwa.2016.03.008\">https://doi.org/10.1016/j.nonrwa.2016.03.008</a>","bibtex":"@article{Black_2016, title={Sublinear signal production in a two-dimensional Keller–Segel–Stokes system}, volume={31}, DOI={<a href=\"https://doi.org/10.1016/j.nonrwa.2016.03.008\">10.1016/j.nonrwa.2016.03.008</a>}, journal={Nonlinear Analysis: Real World Applications}, publisher={Elsevier BV}, author={Black, Tobias}, year={2016}, pages={593–609} }","mla":"Black, Tobias. “Sublinear Signal Production in a Two-Dimensional Keller–Segel–Stokes System.” <i>Nonlinear Analysis: Real World Applications</i>, vol. 31, Elsevier BV, 2016, pp. 593–609, doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2016.03.008\">10.1016/j.nonrwa.2016.03.008</a>.","short":"T. Black, Nonlinear Analysis: Real World Applications 31 (2016) 593–609.","ieee":"T. Black, “Sublinear signal production in a two-dimensional Keller–Segel–Stokes system,” <i>Nonlinear Analysis: Real World Applications</i>, vol. 31, pp. 593–609, 2016, doi: <a href=\"https://doi.org/10.1016/j.nonrwa.2016.03.008\">10.1016/j.nonrwa.2016.03.008</a>.","chicago":"Black, Tobias. “Sublinear Signal Production in a Two-Dimensional Keller–Segel–Stokes System.” <i>Nonlinear Analysis: Real World Applications</i> 31 (2016): 593–609. <a href=\"https://doi.org/10.1016/j.nonrwa.2016.03.008\">https://doi.org/10.1016/j.nonrwa.2016.03.008</a>.","ama":"Black T. Sublinear signal production in a two-dimensional Keller–Segel–Stokes system. <i>Nonlinear Analysis: Real World Applications</i>. 2016;31:593-609. doi:<a href=\"https://doi.org/10.1016/j.nonrwa.2016.03.008\">10.1016/j.nonrwa.2016.03.008</a>"},"year":"2016","volume":31,"author":[{"last_name":"Black","orcid":"0000-0001-9963-0800","id":"23686","full_name":"Black, Tobias","first_name":"Tobias"}],"date_created":"2022-12-21T09:46:31Z","publisher":"Elsevier BV","date_updated":"2022-12-21T10:05:52Z","doi":"10.1016/j.nonrwa.2016.03.008","title":"Sublinear signal production in a two-dimensional Keller–Segel–Stokes system"}]