The Keller–Segel system on bounded convex domains in critical spaces

Matthias Hieber (), Klaus Kress () and Christian Stinner ()
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Matthias Hieber: Technische Universität Darmstadt, Fachbereich Mathematik
Klaus Kress: Technische Universität Darmstadt, Fachbereich Mathematik
Christian Stinner: Technische Universität Darmstadt, Fachbereich Mathematik

Partial Differential Equations and Applications, 2021, vol. 2, issue 3, 1-14

Abstract: Abstract Consider the classical Keller–Segel system on a bounded convex domain $$\varOmega \subset {\mathbb {R}}^3$$ Ω ⊂ R 3 . In contrast to previous works it is not assumed that the boundary of $$\varOmega $$ Ω is smooth. It is shown that this system admits a local, strong solution for initial data in critical spaces which extends to a global one provided the data are small enough in this critical norm. Furthermore, it is shown that this system admits for given T-periodic and sufficiently small forcing functions a unique, strong T-time periodic solution.

Keywords: Keller–Segel system; Convex domains; Critical spaces; Strong periodic solutions; 35Q92; 35K59; 35B10; 47F05; 92C17 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00085-9

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