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The Rayleigh-Bénard problem for compressible fluid flows
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SYSNO ASEP 0567885 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Rayleigh-Bénard problem for compressible fluid flows Author(s) Feireisl, Eduard (MU-W) RID, SAI, ORCID
Świerczewska-Gwiazda, A. (PL)Article number 9 Source Title Archive for Rational Mechanics and Analysis. - : Springer - ISSN 0003-9527
Roč. 247, č. 1 (2023)Number of pages 31 s. Language eng - English Country DE - Germany Keywords compressible fluid flows ; Navier-Stokes system ; Rayleigh-Bénard problem Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA21-02411S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support MU-W - RVO:67985840 UT WOS 000917250800001 EID SCOPUS 85146628525 DOI 10.1007/s00205-022-01837-6 Annotation We consider the physically relevant fully compressible setting of the Rayleigh-Bénard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to gravitational force. Under suitable restrictions imposed on the constitutive relations we show that this open system is dissipative in the sense of Levinson, meaning there exists a bounded absorbing set for any global-in-time weak solution. In addition, global-in-time trajectories are asymptotically compact in suitable topologies and the system possesses a global compact trajectory attractor A. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on A. In addition, the Birkhoff-Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to A a.s. with respect to the invariant measure. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2024 Electronic address https://doi.org/10.1007/s00205-022-01837-6
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