On physically grounded boundary conditions for the compressible MHD system

TL;DR

This paper rigorously justifies physically grounded boundary conditions for the compressible MHD system, establishes the existence of weak solutions, and provides a theoretical basis for numerical experiments on complex domains.

Contribution

It introduces a novel approach using penalization of transport coefficients to analyze singular limits in the compressible MHD system, leading to new boundary conditions and solution existence results.

Findings

Rigorous justification of boundary conditions for compressible MHD.

Existence of weak solutions for arbitrary finite energy data.

Framework for numerical simulations on complex geometries.

Abstract

We consider a general compressible MHD system, where the magnetic field propagates in a heterogeneous medium. Using suitable penalization in terms of the transport coefficients we perform several singular limits. As a result we obtain: 1. A rigorous justification of physically grounded boundary conditions for the compressible MHD system on a bounded domain. 2. Existence of weak solutions for arbitrary finite energy initial data in the situation the Maxwell induction equation holds also outside the fluid domain. 3. A suitable theoretical platform for numerical experiments on domains with geometrically complicated boundaries.