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

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    0575744 - MÚ 2024 RIV DE eng J - Journal Article
    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
    R&D Projects: GA ČR(CZ) GA19-04243S; GA ČR(CZ) GC22-08633J
    Grant - others:AV ČR(CZ) AP2101
    Program: Akademická prémie - Praemium Academiae
    Institutional support: RVO:67985840
    Keywords : compressible fluids * friction * Galerkin method * Navier-Stokes equation
    OECD category: Pure mathematics
    Impact factor: 1.7, year: 2023
    Method of publishing: Open access
    Result website:
    https://doi.org/10.1007/s00033-023-02062-1DOI: 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.
    Permanent Link: https://hdl.handle.net/11104/0345478
     
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