The compressible Navier-Stokes equations with slip boundary conditions of friction type

0575744 - MÚ 2024 RIV DE eng J - Článek v odborném periodiku
Nečasová, Šárka - Ogorzaly, Justyna - Scherz, Jan
The compressible Navier-Stokes equations with slip boundary conditions of friction type.
Zeitschrift für angewandte Mathematik und Physik. Roč. 74, č. 5 (2023), č. článku 188. ISSN 0044-2275. E-ISSN 1420-9039
Grant CEP: GA ČR(CZ) GA19-04243S; GA ČR(CZ) GC22-08633J
Grant ostatní: AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institucionální podpora: RVO:67985840
Klíčová slova: compressible fluids * friction * Galerkin method * Navier-Stokes equation
Obor OECD: Pure mathematics
Impakt faktor: 2, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1007/s00033-023-02062-1

We study a mathematical model of a viscous compressible fluid obeying the slip boundary condition of friction type. We present a notion of weak solutions to this model, in which the momentum equation and the associated energy inequality are combined into a single relation. Moreover, the slip boundary condition of friction type is incorporated into this relation by the use of a boundary integral. Our main result proves the existence of such weak solutions. The proof of this result combines the classical existence theory for the compressible Navier–Stokes equations with an approximation of the aforementioned boundary integral via a convex regularization of the absolute value function.
Trvalý link: https://hdl.handle.net/11104/0345478