Abstract
AbstractIn this paper our goal is to define a renormalized dissipative measure-valued (rDMV) solution of compressible Navier–Stokes system for fluids with non-monotone pressure–density relation. We prove existence of rDMV solutions and establish a suitable relative energy inequality. Moreover we obtain the weak (measure-valued)–strong uniqueness property of this rDMV solution with the help of relative energy inequality.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
Reference18 articles.
1. Antontsev, S.N., Kazhikhov, A.V., Monakhov, V.N.: Kraevye zadachi mekhaniki neodnorodnykh zhidkosteĭ. Nauka. Sibirsk. Otdel., Novosibirsk (1983)
2. Bresch, D., Jabin, P.-E.: Global existence of weak solutions for compressible Navier–Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor. Ann. Math. (2) 188(2), 577–684 (2018)
3. Brezina, J., Feireisl, E., Novotný, A.: Stability of strong solutions to the Navier–Stokes–Fourier system. arXiv e-Prints (Feb. 2018). arXiv:1802.01785
4. Chaudhuri, N.: On weak–strong uniqueness for compressible Navier–Stokes system with general pressure laws. arXiv e-Prints (Nov. 2018). arXiv:1811.08957
5. Dafermos, C.M.: The second law of thermodynamics and stability. Arch. Ration. Mech. Anal. 70, 167–179 (1979)
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