On desingularization of steady vortex in the lake equations

TL;DR

This paper constructs a family of steady vortex solutions for the lake equations, showing they desingularize singular vortices and are localized at the lake's deepest point, with stability and qualitative properties analyzed.

Contribution

It introduces a novel family of vortex solutions for the lake equations that desingularize singular vortices and analyzes their stability and properties.

Findings

Vortex solutions are localized at the lake's deepest point.

Constructed solutions desingularize singular vortices.

Established stability and qualitative properties.

Abstract

We constructed a family of steady vortex solutions for the lake equations with general vorticity function, which constitute a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake. We also study global nonlinear stability for these solutions. Some qualitative and asymptotic properties are also established.