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Low Regularity Solutions for the Surface Quasi-Geostrophic Front Equation

PDE and Applied Math Seminar

Speaker: Albert Ai, University of Wisconsin, Madison
Location: Zoom
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.