Sala Seminari .<\/p>\n
We consider the physically relevant fully compressible setting of the<\/span> Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" 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…<\/p>\n
\nRayleigh-Benard problem of<\/span>
\na fluid confined between two parallel plates, heated from the bottom,<\/span>
\nand subjected to the gravitational force.<\/span>
\nUnder suitable restrictions imposed on the constitutive relations we<\/span>
\nshow that this open system is dissipative in the sense of Levinson,<\/span>
\nmeaning there exists a bounded absorbing set for any global-in-time weak<\/span>
\nsolution. In addition, global-in-time trajectories are asymptotically<\/span>
\ncompact in suitable topologies and the system possesses a global compact<\/span>
\ntrajectory attractor. The standard technique of Krylov and Bogolyubov<\/span>
\nthen yields the existence of an invariant measure – a stationary<\/span>
\nstatistical solution sitting on the global attractor. In addition, the<\/span>
\nBirkhoff–Khinchin ergodic theorem provides convergence of ergodic<\/span>
\naverages of solutions belonging to the attractor a.s. with respect to<\/span>
\nthe invariant measure.<\/span><\/p>\n