Special Session 2: New frontiers in the compressible mathematical fluid mechanics and thermodynamics

Stability and convergence in compressible magnetohydrodynamics
Hana Mizerova
Comenius University in Bratislava
Slovak Rep
Co-Author(s):    
Abstract:
This talk presents recent results on the analysis of the full compressible magnetohydrodynamic system with non-conservative boundary conditions, providing a rigorous bridge between analytical theory and computational practice. Dissipative measure-valued (DMV) solutions are introduced together with a DMV-strong uniqueness principle, ensuring that DMV solutions coincide with strong solutions as long as the latter exist. This stability result provides a robust foundation for numerical analysis. In particular, a structure-preserving finite volume scheme is considered, and the DMV-strong uniqueness principle is employed to prove convergence of numerical solutions to the physically relevant strong solution.