O.-N. Avadanei - Low regularity well-posedness for the generalized surface quasi-geostrophic front..

This talk was part of the Thematic Programme on "Nonlinear Waves and Relativity" held at the ESI April 29 -- June 21, 2024.
We consider the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation. By making use of the null structure of the equation, we carry out a paradifferential normal form analysis in order to obtain balanced energy estimates,
which allows us to prove the local well-posedness of the g-SQG front equation in the non-periodic case at a low level of regularity (in the SQG case, this is only one half of a derivative above scaling). In addition, we establish global well-posedness for small and localized rough initial data, as well as modified scattering, by using the testing by wave packet approach of Ifrim-Tataru.
This is joint work with Albert Ai.