Global solutions to the three-dimensional full compressible magnetohydrodynamic flows

TL;DR

This paper proves the existence of global weak solutions for the complex three-dimensional full compressible magnetohydrodynamic equations with large initial data, considering temperature-dependent viscosity and heat conductivity.

Contribution

It introduces a novel approximation and weak convergence approach to establish global solutions for these highly nonlinear equations with large data.

Findings

Existence of global variational weak solutions is proven.

Solutions accommodate temperature-dependent viscosity and heat conductivity.

The approach handles large initial data effectively.

Abstract

The equations of the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows are considered in a bounded domain. The viscosity coefficients and heat conductivity can depend on the temperature. A solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global variational weak solution to the three-dimensional full magnetohydrodynamic equations with large data is established.