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

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

Hi Jun Choe, Bataa Lkhagvasuren, Minsuk Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2453-2464
Number of pages	12
Journal	Communications on Pure and Applied Analysis
Volume	14
Issue number	6
DOIs	https://doi.org/10.3934/cpaa.2015.14.2453
Publication status	Published - 2015 Nov 1

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.3934/cpaa.2015.14.2453

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

Abstract

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