Well-posedness of compressible magneto-micropolar fluid equations

Abstract

We are concerned with compressible magneto-micropolar fluid equations (1.1)-(1.2). The global existence and large time behaviour of solutions near a constant state to the magneto-micropolar-Navier-Stokes-Poisson (MMNSP) system is investigated in $\mathbb{R}^3$. By a refined energy method, the global existence is established under the assumption that the $H^3$ norm of the initial data is small, but the higher order derivatives can be large. If the initial data belongs to homogeneous Sobolev spaces or homogeneous Besov spaces, we prove the optimal time decay rates of the solution and its higher order spatial derivatives. Meanwhile, we also obtain the usual $L^p-L^2$ $(1\leq p\leq2)$ type of the decay rates without requiring that the $L^p$ norm of initial data is small.