[{"intvolume":"       109","publication_status":"published","date_updated":"2024-04-07T12:36:25Z","publication_identifier":{"issn":["0024-6107","1469-7750"]},"author":[{"full_name":"Wang, Yulan","last_name":"Wang","first_name":"Yulan"},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"title":"An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system","year":"2024","doi":"10.1112/jlms.12885","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional domain  and for a given nondecreasing positive unbounded , for each  and  the inequality\r\n<jats:disp-formula />is shown to hold for any positive  fulfilling\r\n<jats:disp-formula />This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over  near its explosion time.</jats:p>","lang":"eng"}],"publication":"Journal of the London Mathematical Society","issue":"3","type":"journal_article","keyword":["General Mathematics"],"date_created":"2024-04-07T12:27:28Z","status":"public","volume":109,"user_id":"31496","publisher":"Wiley","_id":"53315","citation":{"chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i> 109, no. 3 (2024). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>.","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","apa":"Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>, <i>109</i>(3). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, 2024, doi: <a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","ama":"Wang Y, Winkler M. An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving $L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>}, number={3}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving $L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>."}},{"status":"public","_id":"63259","publisher":"Wiley","volume":109,"user_id":"31496","citation":{"short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","chicago":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i> 109, no. 3 (2024). <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>.","apa":"Wang, Y., &#38; Winkler, M. (2024). An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>, <i>109</i>(3), Article e12885. <a href=\"https://doi.org/10.1112/jlms.12885\">https://doi.org/10.1112/jlms.12885</a>","ieee":"Y. Wang and M. Winkler, “An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, Art. no. e12885, 2024, doi: <a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>.","ama":"Wang Y, Winkler M. An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system. <i>Journal of the London Mathematical Society</i>. 2024;109(3). doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>","bibtex":"@article{Wang_Winkler_2024, title={An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>}, number={3e12885}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Wang, Yulan and Winkler, Michael}, year={2024} }","mla":"Wang, Yulan, and Michael Winkler. “An Interpolation Inequality Involving LlogL$L\\log L$ Spaces and Application to the Characterization of Blow‐up Behavior in a Two‐dimensional Keller–Segel–Navier–Stokes System.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 3, e12885, Wiley, 2024, doi:<a href=\"https://doi.org/10.1112/jlms.12885\">10.1112/jlms.12885</a>."},"publication_identifier":{"issn":["0024-6107","1469-7750"]},"author":[{"first_name":"Yulan","last_name":"Wang","full_name":"Wang, Yulan"},{"id":"31496","last_name":"Winkler","first_name":"Michael","full_name":"Winkler, Michael"}],"year":"2024","title":"An interpolation inequality involving LlogL$L\\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system","intvolume":"       109","publication_status":"published","date_updated":"2025-12-18T20:14:39Z","language":[{"iso":"eng"}],"article_number":"e12885","doi":"10.1112/jlms.12885","issue":"3","publication":"Journal of the London Mathematical Society","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>In a smoothly bounded two‐dimensional domain  and for a given nondecreasing positive unbounded , for each  and  the inequality\r\n<jats:disp-formula/>is shown to hold for any positive  fulfilling\r\n<jats:disp-formula/>This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over  near its explosion time.</jats:p>","lang":"eng"}],"date_created":"2025-12-18T19:07:25Z","type":"journal_article"},{"date_created":"2026-07-08T08:04:28Z","type":"journal_article","publication":"Journal of the London Mathematical Society","issue":"1","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>Affine Bruhat–Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of  parameterizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite‐dimensional vector space, up to homothety. It has first been studied by Goldman and Iwahori as a piecewise‐linear analogue of symmetric spaces. The space of seminorms compactifies the space of norms and admits a natural surjective restriction map from the Berkovich analytification of projective space that factors the natural tropicalization map. Inspired by Payne's result that the analytification is the limit of all tropicalizations, we show that the space of seminorms is the limit of all tropicalized <jats:italic>linear</jats:italic> embeddings  and prove a faithful tropicalization result for compactified linear spaces. The space of seminorms is in fact the tropical linear space associated to the universal realizable valuated matroid.</jats:p>","lang":"eng"}],"article_number":"e12850","language":[{"iso":"eng"}],"doi":"10.1112/jlms.12850","title":"Buildings, valuated matroids, and tropical linear spaces","year":"2023","publication_identifier":{"issn":["0024-6107","1469-7750"]},"author":[{"full_name":"Battistella, Luca","last_name":"Battistella","first_name":"Luca"},{"first_name":"Kevin","last_name":"Kühn","full_name":"Kühn, Kevin"},{"first_name":"Arne","last_name":"Kuhrs","full_name":"Kuhrs, Arne"},{"first_name":"Martin","last_name":"Ulirsch","full_name":"Ulirsch, Martin","id":"114697"},{"full_name":"Vargas, Alejandro","last_name":"Vargas","first_name":"Alejandro"}],"date_updated":"2026-07-08T08:04:43Z","publication_status":"published","intvolume":"       109","citation":{"ieee":"L. Battistella, K. Kühn, A. Kuhrs, M. Ulirsch, and A. Vargas, “Buildings, valuated matroids, and tropical linear spaces,” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 1, Art. no. e12850, 2023, doi: <a href=\"https://doi.org/10.1112/jlms.12850\">10.1112/jlms.12850</a>.","apa":"Battistella, L., Kühn, K., Kuhrs, A., Ulirsch, M., &#38; Vargas, A. (2023). Buildings, valuated matroids, and tropical linear spaces. <i>Journal of the London Mathematical Society</i>, <i>109</i>(1), Article e12850. <a href=\"https://doi.org/10.1112/jlms.12850\">https://doi.org/10.1112/jlms.12850</a>","short":"L. Battistella, K. Kühn, A. Kuhrs, M. Ulirsch, A. Vargas, Journal of the London Mathematical Society 109 (2023).","chicago":"Battistella, Luca, Kevin Kühn, Arne Kuhrs, Martin Ulirsch, and Alejandro Vargas. “Buildings, Valuated Matroids, and Tropical Linear Spaces.” <i>Journal of the London Mathematical Society</i> 109, no. 1 (2023). <a href=\"https://doi.org/10.1112/jlms.12850\">https://doi.org/10.1112/jlms.12850</a>.","mla":"Battistella, Luca, et al. “Buildings, Valuated Matroids, and Tropical Linear Spaces.” <i>Journal of the London Mathematical Society</i>, vol. 109, no. 1, e12850, Wiley, 2023, doi:<a href=\"https://doi.org/10.1112/jlms.12850\">10.1112/jlms.12850</a>.","bibtex":"@article{Battistella_Kühn_Kuhrs_Ulirsch_Vargas_2023, title={Buildings, valuated matroids, and tropical linear spaces}, volume={109}, DOI={<a href=\"https://doi.org/10.1112/jlms.12850\">10.1112/jlms.12850</a>}, number={1e12850}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Battistella, Luca and Kühn, Kevin and Kuhrs, Arne and Ulirsch, Martin and Vargas, Alejandro}, year={2023} }","ama":"Battistella L, Kühn K, Kuhrs A, Ulirsch M, Vargas A. Buildings, valuated matroids, and tropical linear spaces. <i>Journal of the London Mathematical Society</i>. 2023;109(1). doi:<a href=\"https://doi.org/10.1112/jlms.12850\">10.1112/jlms.12850</a>"},"_id":"66358","publisher":"Wiley","user_id":"82981","volume":109,"status":"public"},{"status":"public","user_id":"58312","volume":94,"page":"462-478","_id":"40066","publisher":"Wiley","citation":{"ieee":"R. Bañuelos, K. Bogdan, and T. Luks, “Hardy–Stein identities and square functions for semigroups,” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2, pp. 462–478, 2016, doi: <a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>.","apa":"Bañuelos, R., Bogdan, K., &#38; Luks, T. (2016). Hardy–Stein identities and square functions for semigroups. <i>Journal of the London Mathematical Society</i>, <i>94</i>(2), 462–478. <a href=\"https://doi.org/10.1112/jlms/jdw042\">https://doi.org/10.1112/jlms/jdw042</a>","chicago":"Bañuelos, Rodrigo, Krzysztof Bogdan, and Tomasz Luks. “Hardy–Stein Identities and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i> 94, no. 2 (2016): 462–78. <a href=\"https://doi.org/10.1112/jlms/jdw042\">https://doi.org/10.1112/jlms/jdw042</a>.","short":"R. Bañuelos, K. Bogdan, T. Luks, Journal of the London Mathematical Society 94 (2016) 462–478.","mla":"Bañuelos, Rodrigo, et al. “Hardy–Stein Identities and Square Functions for Semigroups.” <i>Journal of the London Mathematical Society</i>, vol. 94, no. 2, Wiley, 2016, pp. 462–78, doi:<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>.","bibtex":"@article{Bañuelos_Bogdan_Luks_2016, title={Hardy–Stein identities and square functions for semigroups}, volume={94}, DOI={<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>}, number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Bañuelos, Rodrigo and Bogdan, Krzysztof and Luks, Tomasz}, year={2016}, pages={462–478} }","ama":"Bañuelos R, Bogdan K, Luks T. Hardy–Stein identities and square functions for semigroups. <i>Journal of the London Mathematical Society</i>. 2016;94(2):462-478. doi:<a href=\"https://doi.org/10.1112/jlms/jdw042\">10.1112/jlms/jdw042</a>"},"date_updated":"2023-01-26T17:20:19Z","publication_status":"published","intvolume":"        94","year":"2016","title":"Hardy–Stein identities and square functions for semigroups","author":[{"first_name":"Rodrigo","last_name":"Bañuelos","full_name":"Bañuelos, Rodrigo"},{"full_name":"Bogdan, Krzysztof","last_name":"Bogdan","first_name":"Krzysztof"},{"id":"58312","first_name":"Tomasz","last_name":"Luks","full_name":"Luks, Tomasz"}],"publication_identifier":{"issn":["0024-6107","1469-7750"]},"doi":"10.1112/jlms/jdw042","language":[{"iso":"eng"}],"extern":"1","publication":"Journal of the London Mathematical Society","issue":"2","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"555"}],"date_created":"2023-01-25T15:43:14Z"},{"page":"427-450","language":[{"iso":"eng"}],"_id":"66352","publisher":"Wiley","doi":"10.1112/jlms/jdv032","user_id":"82981","volume":92,"status":"public","year":"2015","title":"Tropical geometry of moduli spaces of weighted stable curves","author":[{"id":"114697","full_name":"Ulirsch, Martin","first_name":"Martin","last_name":"Ulirsch"}],"publication_identifier":{"issn":["0024-6107","1469-7750"]},"date_updated":"2026-07-09T07:01:53Z","publication_status":"published","intvolume":"        92","date_created":"2026-07-08T07:24:26Z","type":"journal_article","issue":"2","publication":"Journal of the London Mathematical Society","citation":{"short":"M. Ulirsch, Journal of the London Mathematical Society 92 (2015) 427–450.","chicago":"Ulirsch, Martin. “Tropical Geometry of Moduli Spaces of Weighted Stable Curves.” <i>Journal of the London Mathematical Society</i> 92, no. 2 (2015): 427–50. <a href=\"https://doi.org/10.1112/jlms/jdv032\">https://doi.org/10.1112/jlms/jdv032</a>.","ieee":"M. Ulirsch, “Tropical geometry of moduli spaces of weighted stable curves,” <i>Journal of the London Mathematical Society</i>, vol. 92, no. 2, pp. 427–450, 2015, doi: <a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>.","apa":"Ulirsch, M. (2015). Tropical geometry of moduli spaces of weighted stable curves. <i>Journal of the London Mathematical Society</i>, <i>92</i>(2), 427–450. <a href=\"https://doi.org/10.1112/jlms/jdv032\">https://doi.org/10.1112/jlms/jdv032</a>","bibtex":"@article{Ulirsch_2015, title={Tropical geometry of moduli spaces of weighted stable curves}, volume={92}, DOI={<a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>}, number={2}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Ulirsch, Martin}, year={2015}, pages={427–450} }","ama":"Ulirsch M. Tropical geometry of moduli spaces of weighted stable curves. <i>Journal of the London Mathematical Society</i>. 2015;92(2):427-450. doi:<a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>","mla":"Ulirsch, Martin. “Tropical Geometry of Moduli Spaces of Weighted Stable Curves.” <i>Journal of the London Mathematical Society</i>, vol. 92, no. 2, Wiley, 2015, pp. 427–50, doi:<a href=\"https://doi.org/10.1112/jlms/jdv032\">10.1112/jlms/jdv032</a>."}}]