  We study an initial-boundary value problem of three-dimensional (3D)
compressible isentropic magneto-micropolar fluid equations with Coulomb force
and slip boundary conditions in a bounded simply connected domain, whose
boundary has a finite number of two-dimensional connected components. We derive
the global existence and uniqueness of classical solutions provided that the
initial total energy is suitably small. Our result generalizes the Cauchy
problems of compressible Navier-Stokes equations with Coulomb force (J.
Differential Equations 269: 8468--8508, 2020) and compressible MHD equations
(SIAM J. Math. Anal. 45: 1356--1387, 2013) to the case of bounded domains
although tackling many surface integrals caused by the slip boundary condition
are complex. The main ingredient of this paper is to overcome the strong
nonlinearity caused by Coulomb force, magnetic field, and rotation effect of
micro-particles by applying piecewise-estimate method and delicate analysis
based on the effective viscous fluxes involving velocity and micro-rotational
velocity.

Analysis of PDEs