Global solutions to planar magnetohydrodynamic equations with radiation and large initial data

TL;DR

This paper proves the global existence of solutions for planar magnetohydrodynamic equations with radiation and large initial data, including the novel aspect of constant transport coefficients, and shows the free boundary expands algebraically over time.

Contribution

It establishes the first global existence results for these MHD equations with radiation and large initial data, incorporating constant transport coefficients.

Findings

Free boundary expands at an algebraic rate over time.

Global solutions exist for large initial data with radiation.

Constant transport coefficient is effectively incorporated.

Abstract

A global existence result is established for a free boundary problem of planar magnetohydrodynamic fluid flows with radiation and large initial data. Particularly, it is novelty to embrace the constant transport coefficient. As a by-product, the free boundary is shown to expand outward at an algebraic rate from above in time.