Mathematical theory of compressible magnetohydrodynamics driven by non-conservative boundary conditions

TL;DR

This paper introduces a new weak solution framework for compressible magnetohydrodynamics with large boundary data, applicable to turbulent regimes, and aligns with classical solutions when they exist, motivated by stellar magnetoconvection.

Contribution

It develops a novel concept of weak solutions for MHD equations with non-conservative boundary conditions, enabling global-in-time solvability in turbulent regimes.

Findings

Weak solutions satisfy weak-strong uniqueness.

Solutions are globally solvable in turbulent regimes.

Framework is motivated by stellar magnetoconvection applications.

Abstract

We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime characteristic for turbulence. The weak solutions comply with the weak-strong uniqueness principle; they coincide with the classical solution of the problem as long as the latter exists. The choice of constitutive relations is motivated by applications in stellar magnetoconvection.