Global existence and boundedness for chemotaxis-Navier-Stokes systems  with position-dependent sensitivity in 2D bounded domains

Sachiko Ishida

doi:10.3934/dcds.2015.35.3463

Article Contents

2015, Volume 35, Issue 8: 3463-3482. Doi: 10.3934/dcds.2015.35.3463

This issue Previous Article Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows Next Article On the partitions with Sturmian-like refinements

Global existence and boundedness for chemotaxis-Navier-Stokes systems with position-dependent sensitivity in 2D bounded domains

Sachiko Ishida^1,

1.
Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601

Received: July 31, 2014

Revised: November 30, 2014

Published: May 2017

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Abstract

This paper is concerned with degenerate chemotaxis-Navier-Stokes systems with position-dependent sensitivity on a two dimensional bounded domain. It is known that in the case without a position-dependent sensitivity function, Tao-Winkler (2012) constructed a globally bounded weak solution of a chemotaxis-Stokes system with any porous medium diffusion, and Winkler (2012, 2014) succeeded in proving global existence and stabilization of classical solutions to a chemotaxis-Navier-Stokes system with linear diffusion. The present work shows global existence and boundedness of weak solutions to a chemotaxis-Navier-Stokes system with position-dependent sensitivity for any porous medium diffusion.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35A01, 35D30, 76D05, 92C17.

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