Stationary solutions of the Navier-Stokes-Fourier system in planar domains with impermeable boundary

0531288 - MÚ 2021 RIV NL eng J - Journal Article
Ciuperca, I. S. - Feireisl, Eduard - Jai, M. - Petrov, A.
Stationary solutions of the Navier-Stokes-Fourier system in planar domains with impermeable boundary.
Journal de Mathematiques Pures et Appliquees. Roč. 140, August (2020), s. 110-138. ISSN 0021-7824. E-ISSN 1776-3371
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : Navier-Stokes-Fourier system * stationary solution * inhomogeneous boundary conditions * Trudinger–Moser inequality
OECD category: Pure mathematics
Impact factor: 2.464, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.matpur.2020.06.001

The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant constitutive relations. The equation of state of a real fluid is considered, where the admissible range of density is confined to a bounded interval (hard sphere model). The transport coefficients depend on the temperature in a general way including both gases and liquids behavior. The heart of the paper are new a priori bounds resulting from Trudinger-Moser inequality.
Permanent Link: http://hdl.handle.net/11104/0309976