[{"status":"public","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"}],"type":"journal_article","publication":"Journal of the London Mathematical Society","language":[{"iso":"eng"}],"keyword":["General Mathematics"],"user_id":"31496","_id":"53315","citation":{"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>.","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} }","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>","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>","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>.","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>."},"intvolume":"       109","year":"2024","issue":"3","publication_status":"published","publication_identifier":{"issn":["0024-6107","1469-7750"]},"doi":"10.1112/jlms.12885","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","author":[{"full_name":"Wang, Yulan","last_name":"Wang","first_name":"Yulan"},{"first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"date_created":"2024-04-07T12:27:28Z","volume":109,"publisher":"Wiley","date_updated":"2024-04-07T12:36:25Z"},{"user_id":"31496","_id":"63259","language":[{"iso":"eng"}],"article_number":"e12885","publication":"Journal of the London Mathematical Society","type":"journal_article","status":"public","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"}],"volume":109,"author":[{"first_name":"Yulan","full_name":"Wang, Yulan","last_name":"Wang"},{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"date_created":"2025-12-18T19:07:25Z","publisher":"Wiley","date_updated":"2025-12-18T20:14:39Z","doi":"10.1112/jlms.12885","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","issue":"3","publication_identifier":{"issn":["0024-6107","1469-7750"]},"publication_status":"published","intvolume":"       109","citation":{"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>","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>.","short":"Y. Wang, M. Winkler, Journal of the London Mathematical Society 109 (2024).","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>","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>.","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>."},"year":"2024"},{"citation":{"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} }","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>.","short":"R. Bañuelos, K. Bogdan, T. Luks, Journal of the London Mathematical Society 94 (2016) 462–478.","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>","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>","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>.","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>."},"intvolume":"        94","page":"462-478","publication_status":"published","publication_identifier":{"issn":["0024-6107","1469-7750"]},"doi":"10.1112/jlms/jdw042","date_updated":"2023-01-26T17:20:19Z","author":[{"last_name":"Bañuelos","full_name":"Bañuelos, Rodrigo","first_name":"Rodrigo"},{"first_name":"Krzysztof","last_name":"Bogdan","full_name":"Bogdan, Krzysztof"},{"last_name":"Luks","full_name":"Luks, Tomasz","id":"58312","first_name":"Tomasz"}],"volume":94,"status":"public","type":"journal_article","extern":"1","_id":"40066","user_id":"58312","department":[{"_id":"555"}],"year":"2016","issue":"2","title":"Hardy–Stein identities and square functions for semigroups","publisher":"Wiley","date_created":"2023-01-25T15:43:14Z","publication":"Journal of the London Mathematical Society","keyword":["General Mathematics"],"language":[{"iso":"eng"}]}]