Measure-valued solutions to the complete Euler system revisited

  • Jan BřezinaEmail author
  • Eduard Feireisl


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.


Euler system Measure-valued solution Weak-strong uniqueness Vanishing dissipation limit 

Mathematics Subject Classification

Primary 35L45 Secondary 35Q35 76N15 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrague 1Czech Republic

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