Existence of vortex sheet solutions to the SQG Equation
Edison Cuba, Lucas C. F. Ferreira
TL;DR
This paper proves the existence of stationary vortex sheet solutions for the SQG equation, showing they can be concentrated on perturbed circular curves near critical points, marking a novel theoretical development.
Contribution
It establishes the first known existence of vortex sheet solutions to the SQG equation with solutions concentrated on perturbed circular curves.
Findings
Existence of stationary vortex sheet solutions for SQG.
Solutions are concentrated on curves near non-degenerate critical points.
First known construction of vortex sheets for SQG.
Abstract
This paper addresses the existence of vortex sheets for the SQG equation. More precisely, we construct a family of stationary vortex sheet solutions that are concentrated on curves that are small perturbations of circles centered on a given non-degenerate critical point. To the best of our knowledge, this is a novel result on the existence of vortex sheets to the SQG equation.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Navier-Stokes equation solutions · Nonlinear Waves and Solitons