On weak (measure-valued)-strong uniqueness for compressible  MHD system with   non-monotone pressure law

Yu Liu; Ting Zhang

doi:10.3934/dcdsb.2021307

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2022, Volume 27, Issue 10: 6063-6081. Doi: 10.3934/dcdsb.2021307

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On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law

Yu Liu and
Ting Zhang^,

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China

^* Corresponding author: Ting Zhang
^* Corresponding author: Ting Zhang

Received: June 2021

Revised: November 2021

Early access: January 5, 2022

Published online: January 5, 2022

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Abstract

In this paper, we define a renormalized dissipative measure-valued (rDMV) solution of the compressible magnetohydrodynamics (MHD) equations with non-monotone pressure law. We prove the existence of the rDMV solutions and establish a suitable relative energy inequality. And we obtain the weak (measure-valued)-strong uniqueness property of this rDMV solution with the help of the relative energy inequality.

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Mathematics Subject Classification: 35A01, 35D30, 35Q30, 76W05.

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References

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