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Navier-Stokes-Fourier system with Dirichlet boundary conditions

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    0560286 - MÚ 2023 RIV GB eng J - Journal Article
    Chaudhuri, N. - Feireisl, Eduard
    Navier-Stokes-Fourier system with Dirichlet boundary conditions.
    Applicable Analysis. Roč. 101, č. 12 (2022), s. 4076-4094. ISSN 0003-6811. E-ISSN 1563-504X
    R&D Projects: GA ČR(CZ) GA18-05974S
    Institutional support: RVO:67985840
    Keywords : Dirichlet boundary conditions * Navier-Stokes-Fourier system * weak solution * weak-strong uniqueness
    OECD category: Pure mathematics
    Impact factor: 1.278, year: 2021
    Method of publishing: Open access

    We consider the Navier–Stokes–Fourier system describing the motion of a compressible, viscous, and heat-conducting fluid in a bounded domain (Formula presented.), d = 2, 3, with general non-homogeneous Dirichlet boundary conditions for the velocity and the absolute temperature, with the associated boundary conditions for the density on the inflow part. We introduce a new concept of a weak solution based on the satisfaction of the entropy inequality together with a balance law for the ballistic energy. We show the weak–strong uniqueness principle as well as the existence of global-in-time solutions.
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