The APDE seminar on Monday, 3/20, will be given by Federico Pasqualotto (UC Berkeley) in-person in Evans 732, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: Singularity formation in the Boussinesq equations

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 Boussinesq equations. 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. This is joint work with Tarek Elgindi (Duke University).