Existence of global solutions for a Keller-Segel-fluid equations with nonlinear diffusion

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...

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Bibliographic Details
Published in:arXiv.org 2015-04
Main Authors: Yun-Sung, Chung, Kang, Kyungkeun
Format: Article
Language:English
Subjects:
Cauchy problems
Computational fluid dynamics
Fluid flow
Navier-Stokes equations
Nonlinear equations
Porous media
Swimming
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1504.02274