Singularity formation in the Boussinesq system
Abstract: In this talk, I will first review existing results on singularity formation in incompressible and inviscid fluids. I will then describe a new mechanism for singularity formation in the 2D Boussinesq system. The initial data we choose is smooth except at one point, where it has Hölder continuous first derivatives. Moreover, the singularity mechanism is connected to the classical Rayleigh–Bénard instability. Finally, I will describe how these considerations translate to a novel singularity formation scenario for the 3D incompressible Euler equations. This is joint work with Tarek Elgindi (Duke University).