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arXiv · 2505.11179

On physically grounded boundary conditions for the compressible MHD system

Jan Brezina·Eduard Feireisl
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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.

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Jan Brezina, Eduard Feireisl. 2025-05-16. On physically grounded boundary conditions for the compressible MHD system. https://arxiv.org/abs/2505.11179

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