Invariants States in Stochastically Forced Boussinesq Equations

Explore the intricacies of invariant states in stochastically forced Boussinesq equations in this 56-minute lecture by Juraj Foldes from the University of Virginia. Delve into topics such as boundary conditions, buoyancy-driven convection, hypoellipticity in 2D torus, and the infinite Prandtl limit. Examine the onset of instability, energy stability, and criteria for stability in these complex systems. Investigate stochastic variational problems, numerical simulations, and the Euler-Lagrange equation. Gain insights into the stabilization by noise and its implications for the Boussinesq equations. This talk, part of the School and Workshop on Mixing and Control, offers a comprehensive exploration of advanced mathematical concepts in fluid dynamics and thermodynamics.

Intro
The Boussinesq Equations
Boundary conditions
Buoyancy Driven Convection...
Hypoellipticity in 2D torus
Physical B.C.
Existence and Uniqueness
The infinite Prandtl limit
Questions
Onset of Instability
Energy Stability
Criterion for stability
Stochastic variational problem
Numerical simulations
Euler-Lagrange equation
Stabilization by noise