# Well-posedness of compressible magneto-micropolar fluid equations

## TL;DR

This paper proves the global existence and decay rates of solutions to the compressible magneto-micropolar fluid equations near a constant state, using refined energy methods and Sobolev space analysis.

## Contribution

It establishes the global existence of solutions with small initial data in $H^3$ and derives optimal decay rates in Sobolev and Besov spaces, extending previous results.

## Key findings

- Global existence of solutions under small $H^3$ initial data
- Optimal decay rates in Sobolev and Besov spaces
- Decay rates in $L^p-L^2$ norms without smallness assumption

## 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.