Euler system with a polytropic equation of state as a vanishing viscosity limit

0558263 - MÚ 2023 RIV CH eng J - Journal Article
Feireisl, Eduard - Klingenberg, C. - Markfelder, S.
Euler system with a polytropic equation of state as a vanishing viscosity limit.
Journal of Mathematical Fluid Mechanics. Roč. 24, č. 3 (2022), č. článku 67. ISSN 1422-6928. E-ISSN 1422-6952
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
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s00021-022-00690-7

We consider the Euler system of gas dynamics endowed with the incomplete (e-rho-p) equation of state relating the internal energy a to the mass density rho 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: http://hdl.handle.net/11104/0331996