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

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


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