Nonlinear orbital stability for planar vortex patches

Daomin Cao; Jie Wan; Guodong Wang

doi:10.1090/proc/14077

Nonlinear orbital stability for planar vortex patches

Daomin Cao
, Jie Wan
, Guodong Wang

Guangzhou University
CAS - Institute of Applied Mathematics
University of Chinese Academy of Sciences

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method.

Original language	English
Pages (from-to)	775-784
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	2
DOIs	https://doi.org/10.1090/proc/14077
Publication status	Published - Feb 2019
Externally published	Yes

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title = "Nonlinear orbital stability for planar vortex patches",

abstract = "In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method.",

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AU - Wang, Guodong

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N2 - In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method.

AB - In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is proved. The proof is based on conservation of energy and vorticity, which is an analogue of the classical Liapunov function method.

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DO - 10.1090/proc/14077

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Nonlinear orbital stability for planar vortex patches

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