Local wellposedness of an approximate equation for SQG fronts

TL;DR

This paper establishes local well-posedness for a nonlocal, dispersive, cubically nonlinear equation modeling SQG fronts with small slopes, in Sobolev spaces of order greater than 7/2.

Contribution

It proves local well-posedness for an approximate SQG front evolution equation in Sobolev spaces, advancing understanding of its mathematical properties.

Findings

Well-posedness established for s > 7/2 in Sobolev spaces.

Provides a rigorous foundation for the approximate SQG front model.

Enhances mathematical understanding of dispersive, nonlocal PDEs in geophysical fluid dynamics.

Abstract

We prove local well-posedness in the Sobolev spaces $\dot H^s(\mathbb{T})$, with $s>7/2$, for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of surface quasi-geostrophic (SQG) fronts with small slopes.