Existence of smooth solutions to coupled chemotaxis-fluid equations

Myeongju Chae, Kyungkeun Kang, Jihoon Lee

Research output: Contribution to journalArticle

81 Citations (Scopus)

Abstract

We consider a system coupling the parabolic-parabolic chemotaxis equations to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criterions. For two dimensional chemotaxis-Navier-Stokes equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observations in [21] on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with stronger restriction on the consumption rate and chemotactic sensitivity.

Original languageEnglish
Pages (from-to)2271-2297
Number of pages27
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume33
Issue number6
DOIs
Publication statusPublished - 2013 Jun 1

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Regular Solution
Chemotaxis
Smooth Solution
Navier Stokes equations
Three-dimension
Blow-up Criterion
Fluid
Global Weak Solutions
Fluids
Local Existence
Incompressible Navier-Stokes Equations
Two Dimensions
Navier-Stokes Equations
Restriction
Observation

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Existence of smooth solutions to coupled chemotaxis-fluid equations. / Chae, Myeongju; Kang, Kyungkeun; Lee, Jihoon.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 33, No. 6, 01.06.2013, p. 2271-2297.

Research output: Contribution to journalArticle

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