On desingularization of steady vortex in the lake equations

2019/11/04 by Daomin Cao, Cao, Daomin, Weicheng Zhan +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.01037

openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Asymptotic estimates for the plasma problem
• A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma
• Desingularization of vortices for 2D steady Euler flows via the vorticity method

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