On weak-strong uniqueness property for the full compressible magnetohydrodynamics flows

TL;DR

This paper investigates the weak-strong uniqueness property for full compressible magnetohydrodynamics flows, demonstrating that weak solutions coincide with strong solutions originating from the same initial data using relative entropy methods.

Contribution

It establishes the weak-strong uniqueness for full compressible MHD flows using a relative entropy approach, extending previous results to more complex flow models.

Findings

Weak solutions coincide with strong solutions when both exist from the same initial data.

The relative entropy inequality is effectively used to prove uniqueness.

Results apply to flows influenced by magnetic fields, gravity, and compressibility.

Abstract

This paper is devoted to the study of the weak-strong uniqueness property for the full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and with an additional equation which describes the evolution of the magnetic field. Using relative entropy inequality, we prove that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists.