Collected Papers in Honor of Yoshihiro Shibata

0573348 - MÚ 2024 RIV CH eng M - Monography Chapter
Feireisl, Eduard - Klingenberg, C. - Markfelder, S.
Euler system with a polytropic equation of state as a vanishing viscosity limit.
Collected Papers in Honor of Yoshihiro Shibata. Cham: Birkhäuser, 2022 - (Ozawa, T.), s. 89-110. ISBN 978-3-031-19251-7
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : polytropic equation of state * compressible Euler system * Navier-Stokes-Fourier system * vanishing dissipation limit
OECD category: Pure mathematics
https://doi.org/10.1007/978-3-031-19252-4_5

We consider the Euler system of gas dynamics endowed with the incomplete (e-ρ-p) equation of state relating the internal energy e to the mass density ρ and the pressure p. We show that any sufficiently smooth solution can be recovered as a vanishing viscosity-heat conductivity limit of the Navier-Stokes-Fourier system with a properly defined temperature. The result is unconditional in the case of the Navier type (slip) boundary conditions and extends to the no-slip condition for the velocity under some extra hypotheses of Kato’s type concerning the behavior of the fluid in the boundary layer.
Permanent Link: https://hdl.handle.net/11104/0343810