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Bae, Hantaek
School of Natural Science
Research Interests
  • Fluid dynamics, polymeric fluid, kinetic theory

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Local and global existence of solutions of a Keller-Segel model coupled to the incompressible fluid equations

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Title
Local and global existence of solutions of a Keller-Segel model coupled to the incompressible fluid equations
Author
Bae, HantaekKang, Kyungkeun
Issue Date
2022-10
Publisher
Academic Press
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.333, pp.407 - 435
Abstract
We consider a Keller-Segel model coupled to the incompressible fluid equations which describes the dynamics of swimming bacteria. We mainly take the incompressible Navier-Stokes equations for the fluid equation part. In this case, we first show the existence of unique local-in-time solutions for large data in scaling invariant Besov spaces. We then proceed to show that these solutions can be defined globally-in-time if some smallness conditions are imposed to initial data. We also show the existence of unique global-in-time self-similar solutions when initial data are sufficiently small in scaling invariant Besov spaces. But, these solutions do not exhibit (expected) temporal decay rates. So, we change the fluid part to the Stokes equations and we derive temporal decay rates of the bacteria density and the fluid velocity.
URI
https://scholarworks.unist.ac.kr/handle/201301/58809
DOI
10.1016/j.jde.2022.06.010
ISSN
0022-0396
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MTH_Journal Papers
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