Global well-posedness for 3D incompressible inhomogeneous asymmetric fluids with density-dependent viscosity

Abstract

In this paper, we investigate the 3D inhomogeneous incompressible asymmetric fluids system with density-dependent viscosity. By the assumption of the smallness of initial velocity in the critical Besov space, B˙p,13/p−1 for 1<p<6 and the initial density in the critical Besov space and bounded away from vacuum, the local and global well-posedness of 3D inhomogeneous incompressible asymmetric fluids is obtained. By giving the different estimates for pressure in the system for 1<p<32 and 32≤p<6, it shows the a priori estimate for the corresponding linearized equation. This not only improves the previous results for 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity, but also obtains the new results on the micropolar system without smallness for density in critical Besov spaces.