Global existence and large time behavior of classical solutions to the two‐dimensional micropolar equations with large initial data and vacuum

Abstract

This paper concerns the global existence and large time behavior of classical, strong, and weak solutions to the two‐dimensional compressible micropolar equations with large initial data and vacuum. We assume that the shear and angular viscosity coefficients are positive constants and the bulk coefficient is , where ρ is the density and β > 3/2. It is crucial to derive an upper bound of the density uniformly in the time such that all the classical, strong, and weak solutions converge to the equilibrium state as the time tends to infinity.