Title: Long time behavior of solutions to open fluid systems, Speaker(s): Prof. Eduard Feireisl, Institute of Mathematics, Czech Academy of Sciences, Date and time: 25 May 2022, 17:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: room Sala Seminari.

You can access the full event here: https://events.dm.unipi.it/e/93

Abstract --------

We consider the physically relevant fully compressible setting of the Rayleigh-Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the 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. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on the global attractor. In addition, the Birkhoff--Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to the attractor a.s. with respect to the invariant measure.

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