Global existence and exponential decay of strong solutions for 2D nonhomogeneous micropolar fluids with density-dependent viscosity

Abstract

We study an initial boundary value problem of two-dimensional nonhomogeneous micropolar fluid equations with density-dependent viscosity and non-negative density. Applying the Desjardins interpolation inequality and delicate energy estimates, we show the global existence of a unique strong solution under the condition that $\Vert \nabla \mu ({\rho }_0){\Vert }_{L^q}$ is suitably small. Moreover, we prove that the velocity and the micro-rotational velocity converge exponentially to zero in H² as time goes to infinity.