Voigt Boussinesq Equations - Global Regularity and Fluid Dynamics

Explore the Voigt Boussinesq equations in this 45-minute conference talk from the Workshop on Geometry and Analysis of Fluid Flows. Delve into the complexities of incompressible fluid equations, focusing on the Boussinesq equations and their connection to thermal convection. Examine the open problem of finite time singularities in ideal 2D Boussinesq equations and its relation to 3D Euler equations. Learn about the Voigt Boussinesq approximation, its features, and a global regularity result for critical Voigt Boussinesq equations. Gain insights into local and global existence, well-posedness, and approximation in incompressible fluids equations. Follow the presentation's structure, covering topics such as ideal incompressible fluids, SQG example, blow-up problems, Voigt approximations, and the main result of global regularity. Understand the ideas behind the proof, including local existence, basic energy structure, and the Boussinesq limit.

Ideal Incompressible Fluids
Analogies with the 3D incompressible Euler equations
Local existence, uniqueness, extension
The SQG example
Beyond local existence, BKM
Leray approximations: the example of SQG
The 2D Boussinesq system
The Blow up problem
Voigt approximations
2D Voigt Boussinesq Equations
Main Result: Global Regularity
Limit of Vanishing Regularization
Fractional Voigt Boussinesq
Ideas of Proof: local existence
Basic Energy Structure
Ideas of proof: global existence for 1
Ideas of proof: BKM
Ideas of Proof: global regularity
Ideas of Proof: Boussinesq limit, continued