Low Regularity Well-Posedness for the Generalized Surface Quasi-Geostrophic Front Equation

Explore a 14-minute conference talk on the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation, presented as part of the Thematic Programme on "Nonlinear Waves and Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the speaker's approach using paradifferential normal form analysis to obtain balanced energy estimates, leading to local well-posedness in the non-periodic case at a low level of regularity. Learn about the establishment of global well-posedness for small and localized rough initial data, as well as modified scattering, through the application of the Ifrim-Tataru testing by wave packet approach. Gain insights into this joint work with Albert Ai, which addresses the SQG case with only one half of a derivative above scaling.