Special Session 2: New frontiers in the compressible mathematical fluid mechanics and thermodynamics

Mach, Rossby and the Rayleigh-B\`enard problem
Francesco Fanelli
Basque Center for Applied Mathematics
Spain
Co-Author(s):    
Abstract:
In this talk, we revisit some recent results about the dynamics of heat conducting fluids in the incompressible limit regime, under non-homogeneous boundary conditions for the temperature (a relevant situation in the context of the celebrated Rayleigh-B\`enard problem). We show how the classical Oberbeck-Boussinesq system, usually identified as the target system, must be modified in this case, or even dismissed in presence of additional fast rotation effects. This talk is based on joint works with Eduard Feireisl (Czech Academy of Sciences).