Wellposedness of the Keller-Segel Navier-Stokes equations in the critical Besov spaces

Hi Jun Choe; Bataa  Lkhagvasuren; Minsuk  Yang

doi:10.3934/cpaa.2015.14.2453

Article Contents

2015, Volume 14, Issue 6: 2453-2464. Doi: 10.3934/cpaa.2015.14.2453

This issue Previous Article Regularity and nonexistence of solutions for a system involving the fractional Laplacian Next Article Global existence and blow up of solutions to a class of pseudo-parabolic equations with an exponential source

Wellposedness of the Keller-Segel Navier-Stokes equations in the critical Besov spaces

1.
Department of Mathematics, Yonsei University, 120-749 SeoDaeMun-gu, Seoul
2.
Mathematics Department,Yonsei University, Seoul 120-749
3.
School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722

Received: March 31, 2015

Revised: June 30, 2015

Published: October 2015

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Abstract

We consider the Keller-Segel model coupled with the incompressible Navier-Stokes equations in dimension three. We prove the local in time existence of the solution for large initial data and the global in time existence of the solution for small initial data plus some smallness condition on the gravitational potential in the critical Besov spaces, which are new results for the model.

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Mathematics Subject Classification: 35Kxx, 35Qxx, 76Dxx, 76Zxx.

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