Uniform regularity and vanishing viscosity limit for the chemotaxis‐Navier‐Stokes system in a 3D bounded domain |
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Authors: | Zhipeng Zhang |
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Affiliation: | Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China |
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Abstract: | We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis‐Navier‐Stokes system with Navier boundary condition for velocity field and Neumann boundary condition for cell density and chemical concentration in a 3D bounded domain. It is shown that there exists a unique strong solution of the incompressible chemotaxis‐Navier‐Stokes system in a finite time interval, which is independent of the viscosity coefficient. Moreover, this solution is uniformly bounded in a conormal Sobolev space, which allows us to take the vanishing viscosity limit to obtain the incompressible chemotaxis‐Euler system. |
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Keywords: | conormal Sobolev space incompressible chemotaxis‐Navier‐Stokes system Navier boundary condition vanishing viscosity limit |
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