Non-contraction of intermediate admissible discontinuities for 3-D planar isentropic magnetohydrodynamics

TL;DR

This paper studies the stability of shock waves and contact discontinuities in 3D planar isentropic MHD, demonstrating non-contraction of large perturbations using relative entropy methods.

Contribution

It extends the analysis of non-contraction properties to three-dimensional isentropic MHD, utilizing criteria based on relative entropy and pseudo distances.

Findings

Large perturbations around intermediate shocks do not contract.

Non-contraction is established using relative entropy criteria.

Results apply to 3D planar isentropic MHD shock waves.

Abstract

We investigate non-contraction of large perturbations around intermediate entropic shock waves and contact discontinuities for the three-dimensional planar compressible isentropic magnetohydrodynamics (MHD). To do that, we take advantage of criteria developed by Kang and Vasseur in [6], and non-contraction property is measured by pseudo distance based on relative entropy.