Low Regularity Solutions for the Surface Quasi-Geostrophic Front EquationPDE and Applied Math Seminar
|Speaker:||Albert Ai, University of Wisconsin, Madison|
|Start time:||Thu, Oct 12 2023, 4:10PM|
In this talk, we consider the local well-posedness of the surface quasi-geostrophic (SQG) front equation in low regularity Sobolev spaces. By observing a null structure for the equation, we obtain access to a normal form transformation. 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.