On physically grounded boundary conditions for the compressible MHD system

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.