On desingularization of steady vortex in the lake equations

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.