Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains

0483129 - MÚ 2018 RIV NL eng J - Journal Article
Kreml, Ondřej - Mácha, Václav - Nečasová, Šárka - Wróblewska-Kamińska, A.
Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains.
Journal de Mathematiques Pures et Appliquees. Roč. 109, January (2018), s. 67-92. ISSN 0021-7824. E-ISSN 1776-3371
R&D Projects: GA ČR GA13-00522S; GA MŠMT(CZ) 7AMB16PL060
Institutional support: RVO:67985840
Keywords : compressible Navier–Stokes–Fourier equations * time-varying domain * slip boundary conditions
OECD category: Pure mathematics
Impact factor: 1.961, year: 2018
http://www.sciencedirect.com/science/article/pii/S0021782417301381?via%3Dihub

We consider the compressible Navier–Stokes–Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an elastic part and a thermal part, we prove global-in-time existence of weak solutions. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, the thermal energy equation is in the weak formulation replaced by the thermal energy inequality complemented with the global total energy inequality. In the approximation scheme the thermal energy inequality is considered to be satisfied in the renormalized sense.
Permanent Link: http://hdl.handle.net/11104/0278535