Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

TL;DR

This paper proves the global existence and analyzes the large-time behavior of weak solutions to 3D compressible magnetohydrodynamic flows with large initial data, using energy estimates and weak convergence methods.

Contribution

It establishes the existence and long-term behavior of solutions for the 3D compressible MHD equations with large data, a significant extension over previous results.

Findings

Global weak solutions exist for the considered equations.

Solutions exhibit specific large-time decay properties.

The analysis applies to flows with large initial data and constant viscosity.

Abstract

The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $\gamma>\frac32$ and constant viscosity coefficients.