Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations
Analysis of PDEs
2012-02-21 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1112.4566,
title = {Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations},
author = {Myeongju Chae and Kyungkeun Kang and Jihoon Lee},
journal= {arXiv preprint arXiv:1112.4566},
year = {2012}
}