Global well-posedness and exponential decay of strong solution for the three-dimensional inhomogeneous incompressible micropolar equations with density-dependent transport coefficients and large initial data

Abstract

In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we establish the global existence of strong solutions as long as the initial density is linear equivalent to a large constant state. There is no restriction on the size of initial velocity and micro-rotational velocity. As a by-product, we prove the exponential decay for the solution.