On desingularization of steady vortex for the lake equations

Abstract In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake....

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 87; no. 1; pp. 50 - 79
Main Authors Cao, Daomin, Zhan, Weicheng, Zou, Changjun
Format Journal Article
LanguageEnglish
Published Oxford University Press 22.01.2022
Subjects
steady vortex solutions
maximizer
elliptic equations
desingularization
variational method
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Summary:Abstract In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes 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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxab042