Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion

Yun Sung Chung, Kyungkeun Kang

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Article number041503
JournalJournal of Mathematical Physics
Volume57
Issue number4
DOIs
Publication statusPublished - 2016 Apr 1

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Chemotaxis
Nonlinear Diffusion
Global Solution
Fluid
Stokes System
Cauchy problem
Navier-Stokes System
Existence of Weak Solutions
fluids
Bacteria
Navier-Stokes equation
Coupled System
bacteria
Porous Media
Weak Solution
Three-dimension
Oxygen
Cauchy Problem
Navier-Stokes Equations
Motion

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Existence of global solutions for a chemotaxis-fluid system with nonlinear diffusion. / Chung, Yun Sung; Kang, Kyungkeun.

In: Journal of Mathematical Physics, Vol. 57, No. 4, 041503, 01.04.2016.

Research output: Contribution to journalArticle

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