{"intvolume":" 169","date_created":"2025-12-18T19:47:51Z","date_updated":"2025-12-18T19:57:40Z","publication_identifier":{"issn":["0167-8019","1572-9036"]},"volume":169,"type":"journal_article","status":"public","author":[{"id":"31496","first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael"}],"doi":"10.1007/s10440-020-00312-2","publication_status":"published","language":[{"iso":"eng"}],"abstract":[{"text":"AbstractIn a bounded planar domain $\\varOmega $\r\n Ω\r\n with smooth boundary, the initial-boundary value problem of homogeneous Neumann type for the Keller-Segel-fluid system \r\n\t\t\t $$\\begin{aligned} \\left \\{ \\textstyle\\begin{array}{l@{\\quad }l} n_{t} + \\nabla \\cdot (nu) = \\Delta n - \\nabla \\cdot (n\\nabla c), & x\\in \\varOmega , \\ t>0, \\\\ 0 = \\Delta c -c+n, & x\\in \\varOmega , \\ t>0, \\end{array}\\displaystyle \\right . \\end{aligned}$$ \r\n \r\n {\r\n \r\n \r\n \r\n \r\n n\r\n t\r\n \r\n +\r\n ∇\r\n ⋅\r\n (\r\n n\r\n u\r\n )\r\n =\r\n Δ\r\n n\r\n −\r\n ∇\r\n ⋅\r\n (\r\n n\r\n ∇\r\n c\r\n )\r\n ,\r\n \r\n \r\n x\r\n ∈\r\n Ω\r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n 0\r\n =\r\n Δ\r\n c\r\n −\r\n c\r\n +\r\n n\r\n ,\r\n \r\n \r\n x\r\n ∈\r\n Ω\r\n ,\r\n \r\n t\r\n >\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n is considered, where $u$\r\n u\r\n is a given sufficiently smooth velocity field on $\\overline {\\varOmega }\\times [0,\\infty )$\r\n \r\n Ω\r\n ‾\r\n \r\n ×\r\n [\r\n 0\r\n ,\r\n ∞\r\n )\r\n that is tangential on $\\partial \\varOmega $\r\n ∂\r\n Ω\r\n but not necessarily solenoidal.It is firstly shown that for any choice of $n_{0}\\in C^{0}(\\overline {\\varOmega })$\r\n \r\n n\r\n 0\r\n \r\n ∈\r\n \r\n C\r\n 0\r\n \r\n (\r\n \r\n Ω\r\n ‾\r\n \r\n )\r\n with $\\int _{\\varOmega}n_{0}<4\\pi $\r\n \r\n ∫\r\n Ω\r\n \r\n \r\n n\r\n 0\r\n \r\n <\r\n 4\r\n π\r\n , this problem admits a global classical solution with $n(\\cdot ,0)=n_{0}$\r\n n\r\n (\r\n ⋅\r\n ,\r\n 0\r\n )\r\n =\r\n \r\n n\r\n 0\r\n \r\n , and that this solution is even bounded whenever $u$\r\n u\r\n is bounded and $\\int _{\\varOmega}n_{0}<2\\pi $\r\n \r\n ∫\r\n Ω\r\n \r\n \r\n n\r\n 0\r\n \r\n <\r\n 2\r\n π\r\n . Secondly, it is seen that for each $m>4\\pi $\r\n m\r\n >\r\n 4\r\n π\r\n one can find a classical solution with $\\int _{\\varOmega}n(\\cdot ,0)=m$\r\n \r\n ∫\r\n Ω\r\n \r\n n\r\n (\r\n ⋅\r\n ,\r\n 0\r\n )\r\n =\r\n m\r\n which blows up in finite time, provided that $\\varOmega $\r\n Ω\r\n satisfies a technical assumption requiring $\\partial \\varOmega $\r\n ∂\r\n Ω\r\n to contain a line segment.In particular, this indicates that the value $4\\pi $\r\n 4\r\n π\r\n of the critical mass for the corresponding fluid-free Keller-Segel system is left unchanged by any fluid interaction of the considered type, thus marking a considerable contrast to a recent result revealing some fluid-induced increase of critical blow-up masses in a related Cauchy problem in the entire plane.","lang":"eng"}],"issue":"1","publication":"Acta Applicandae Mathematicae","publisher":"Springer Science and Business Media LLC","user_id":"31496","_id":"63342","title":"Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?","citation":{"mla":"Winkler, Michael. “Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?” Acta Applicandae Mathematicae, vol. 169, no. 1, Springer Science and Business Media LLC, 2020, pp. 577–91, doi:10.1007/s10440-020-00312-2.","ieee":"M. Winkler, “Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?,” Acta Applicandae Mathematicae, vol. 169, no. 1, pp. 577–591, 2020, doi: 10.1007/s10440-020-00312-2.","bibtex":"@article{Winkler_2020, title={Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?}, volume={169}, DOI={10.1007/s10440-020-00312-2}, number={1}, journal={Acta Applicandae Mathematicae}, publisher={Springer Science and Business Media LLC}, author={Winkler, Michael}, year={2020}, pages={577–591} }","ama":"Winkler M. Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains? Acta Applicandae Mathematicae. 2020;169(1):577-591. doi:10.1007/s10440-020-00312-2","short":"M. Winkler, Acta Applicandae Mathematicae 169 (2020) 577–591.","apa":"Winkler, M. (2020). Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains? Acta Applicandae Mathematicae, 169(1), 577–591. https://doi.org/10.1007/s10440-020-00312-2","chicago":"Winkler, Michael. “Can Fluid Interaction Influence the Critical Mass for Taxis-Driven Blow-up in Bounded Planar Domains?” Acta Applicandae Mathematicae 169, no. 1 (2020): 577–91. https://doi.org/10.1007/s10440-020-00312-2."},"year":"2020","page":"577-591"}