Well-posedness for the surface quasi-geostrophic front equation

2022/11/30 by Ai, Albert, Avadanei, Ovidiu-Neculai · 3 citations
#35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.00117

Abstract

We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter-Shu-Zhang [9] established well-posedness under a small data condition as well as a convergence condition on an expansion of the equation's nonlinearity. In the present article, we establish unconditional large data local well-posedness of the SQG front equation, while also improving the low regularity threshold for the initial data. In addition, we establish global well-posedness theory in the rough data regime by using the testing by wave packet approach of Ifrim-Tataru.

Cited by

• Modified Scattering for Nonlocal Nonlinear Schrödinger Equations
• Homogeneous steady states for the generalized surface quasi-geostrophic equations
• Modified Scattering and Asymptotic Completeness for the Derivative Nonlinear Schrödinger equation

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