Uniform Regularity and Vanishing Viscosity limit for the chemotaxis-Navier-Stokes system in a 3D bounded domain

Abstract

We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis-Navier-Stokes system in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. 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, the solution is uniformly bounded in a conormal Sobolev space, which allows us to take the vanishing viscosity limit to obtain the incompressible inviscid chemotaxis-Navier-Stokes system.