The Rayleigh-Bénard problem for compressible fluid flows

0567885 - MÚ 2024 RIV DE eng J - Journal Article
Feireisl, Eduard - Świerczewska-Gwiazda, A.
The Rayleigh-Bénard problem for compressible fluid flows.
Archive for Rational Mechanics and Analysis. Roč. 247, č. 1 (2023), č. článku 9. ISSN 0003-9527. E-ISSN 1432-0673
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : compressible fluid flows * Navier-Stokes system * Rayleigh-Bénard problem
OECD category: Pure mathematics
Impact factor: 2.5, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00205-022-01837-6

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.
Permanent Link: https://hdl.handle.net/11104/0339143