Measure-valued solutions to the complete Euler system revisited

Jan Březina, Eduard Feireisl

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3 Citations (Scopus)

Abstract

We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier–Stokes–Fourier system. Our main result states that any sequence of weak solutions to the Navier–Stokes–Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.

Original languageEnglish
Article number57
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume69
Issue number3
DOIs
Publication statusPublished - Jun 1 2018
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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