Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations

Details Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations

2011-12-20

arxiv.org/abs/1112.4566v2

Mathematics

Analysis of PDEs

Scientific paper

We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria. For two dimensional Navier-Stokes-Keller-Segel equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observation in [20] on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with rather restrictive consumption rate and chemotactic sensitivity.

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