English

On physically grounded boundary conditions for the compressible MHD system

Analysis of PDEs 2025-05-19 v1

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.

Keywords

Cite

@article{arxiv.2505.11179,
  title  = {On physically grounded boundary conditions for the compressible MHD system},
  author = {Jan Brezina and Eduard Feireisl},
  journal= {arXiv preprint arXiv:2505.11179},
  year   = {2025}
}