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.
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}
}