The APDE seminar on Monday, 12/4, will be given by Albert Ai (UW Madison) in-person in Evans 736, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (firstname.lastname@example.org) or Mengxuan Yang (email@example.com).
Title: Low Regularity Solutions for the Surface Quasi-Geostrophic Front Equation
Abstract: In this talk, we consider the well-posedness of the surface quasi-geostrophic (SQG) front equation in low regularity Sobolev spaces. By observing a null structure, we obtain access to a normal form transformation for the equation. Applying this normal form in the context of a paradifferential analysis with modified energies, we are able to prove balanced cubic energy estimates and thus local well-posedness at just half a derivative above the scaling-critical regularity threshold. This is joint work with Ovidiu-Neculai Avadanei.