Existence of global solutions for a Keller-Segel-fluid equations with nonlinear diffusion
Analysis of PDEs
2016-05-04 v1
Abstract
We consider a coupled system consisting of the Navier-Stokes equations and a porous medium type of Keller-Segel system that model the motion of swimming bacteria living in fluid and consuming oxygen. We establish the global-in-time existence of weak solutions for the Cauchy problem of the system in dimension three. In addition, if the Stokes system, instead Navier-Stokes system, is considered for the fluid equation, we prove that bounded weak solutions exist globally in time.
Keywords
Cite
@article{arxiv.1504.02274,
title = {Existence of global solutions for a Keller-Segel-fluid equations with nonlinear diffusion},
author = {Yun-Sung Chung and Kyungkeun Kang},
journal= {arXiv preprint arXiv:1504.02274},
year = {2016}
}
Comments
24pages