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A model of a nonisothermal two-phase flow of compressible fluids

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    0572038 - MÚ 2024 RIV US eng J - Journal Article
    Feireisl, Eduard - Petcu, M. - She, Bangwei
    A model of a nonisothermal two-phase flow of compressible fluids.
    Mathematical Methods in the Applied Sciences. Roč. 46, č. 8 (2023), s. 9362-9377. ISSN 0170-4214. E-ISSN 1099-1476
    R&D Projects: GA MŠk(CZ) 8J20FR007
    Institutional support: RVO:67985840
    Keywords : Allen-Cahn equation * compressible fluid * Navier-Stokes-Fourier system * two-phase flow
    OECD category: Pure mathematics
    Impact factor: 2.900, year: 2022
    Method of publishing: Limited access

    We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We introduce a suitable weak formulation of the problem based on a combination of the entropy inequality with the total energy conservation principle. Finally, we show compactness of any bounded family of weak solutions and establish a global existence result.
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