Measure-valued solutions to the complete Euler system revisited

0489594 - MÚ 2019 RIV CH eng J - Journal Article
Březina, J. - Feireisl, Eduard
Measure-valued solutions to the complete Euler system revisited.
Zeitschrift für angewandte Mathematik und Physik. Roč. 69, č. 3 (2018), č. článku 57. ISSN 0044-2275. E-ISSN 1420-9039
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : Euler system * measure-valued solution * vanishing dissipation limit
OECD category: Pure mathematics
Impact factor: 1.618, year: 2018
https://link.springer.com/article/10.1007/s00033-018-0951-8

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.
Permanent Link: http://hdl.handle.net/11104/0283977