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Measure-valued solutions to the complete Euler system revisited

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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.

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Authors and Affiliations

  1. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8550, Japan

    Jan Březina

  2. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic

    Eduard Feireisl

Authors
  1. Jan Březina
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  2. Eduard Feireisl
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Correspondence to Jan Březina.

Additional information

The research of E.F. leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement 320078. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO: 67985840.

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Březina, J., Feireisl, E. Measure-valued solutions to the complete Euler system revisited. Z. Angew. Math. Phys. 69, 57 (2018). https://doi.org/10.1007/s00033-018-0951-8

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