Measure-valued solutions to the complete Euler system revisited

0489594 - MÚ 2019 RIV CH eng J - Článek v odborném periodiku
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
GRANT EU: European Commission(XE) 320078 - MATHEF
Institucionální podpora: RVO:67985840
Klíčová slova: Euler system * measure-valued solution * vanishing dissipation limit
Obor OECD: Pure mathematics
Impakt faktor: 1.618, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0283977