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

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