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.