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

Yun Sung Chung, Kyungkeun Kang

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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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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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