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

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

2012-03-12

arxiv.org/abs/1203.2405v2

Mathematics

Analysis of PDEs

arXiv admin note: text overlap with arXiv:1111.4256

Scientific paper

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.

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