The Rayleigh-Bénard problem for compressible fluid flows

0567885 - MÚ 2024 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA21-02411S
Institucionální podpora: RVO:67985840
Klíčová slova: compressible fluid flows * Navier-Stokes system * Rayleigh-Bénard problem
Obor OECD: Pure mathematics
Impakt faktor: 2.5, rok: 2022
Způsob publikování: 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.
Trvalý link: https://hdl.handle.net/11104/0339143