Global classical solution for three-dimensional compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary condition in bounded domains

TL;DR

This paper proves the global existence and uniqueness of classical solutions for 3D compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in bounded domains, extending previous results to more complex boundary conditions.

Contribution

It generalizes existing results on compressible Navier-Stokes and MHD equations to bounded domains with slip boundary conditions, handling complex surface integrals and nonlinearities.

Findings

Established global classical solutions under small initial energy.

Extended analysis techniques to handle Coulomb force and micro-rotation effects.

Overcame nonlinear challenges posed by magnetic and Coulomb forces in bounded domains.

Abstract

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.