Well-posedness for SQG sharp fronts with unbounded curvature

TL;DR

This paper proves local well-posedness for SQG sharp fronts with unbounded curvature in low regularity Sobolev spaces, advancing understanding of temperature front dynamics in geophysical flows.

Contribution

It establishes the well-posedness of SQG sharp fronts with unbounded curvature in low Sobolev regularity spaces, a significant extension over previous results.

Findings

Well-posedness proven for low regularity fronts

Allows for fronts with unbounded curvature

Extends mathematical understanding of SQG dynamics

Abstract

Patch solutions for the surface quasigeostrophic (SQG) equation model sharp temperature fronts in atmospheric and oceanic flows. We establish local well-posedness for SQG sharp fronts of low Sobolev regularity, $H^{2+s}$ for arbitrarily small $s>0$, allowing for fronts with unbounded curvature.