Low regularity well-posedness for the generalized surface quasi-geostrophic front equation

2023/11/13 by Ai, Albert, Avadanei, Ovidiu-Neculai · 1 citation
#35B65 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.07551

Abstract

We consider the well-posedness of the generalized surface quasi-geostrophic (gSQG) front equation. By using the null structure of the equation via a paradifferential normal form analysis, we obtain balanced energy estimates, which allow us to prove the local well-posedness of the non-periodic gSQG front equation at a low level of regularity (in the SQG case, at only one-half derivatives 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.

Cited by

• Modified Scattering and Asymptotic Completeness for the Derivative Nonlinear Schrödinger equation

Related

• Well-posedness for the surface quasi-geostrophic front equation
• Low regularity solutions for the surface quasi-geostrophic front equation
• Well-posedness for SQG sharp fronts with unbounded curvature
• Two-Front Solutions of the SQG Equation and its Generalizations
• Global solutions for a family of GSQG front equations