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

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


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