Compactness and stability for planar vortex-pairs with prescribed impulse

G. R. Burton

doi:10.1016/j.jde.2020.08.009

Compactness and stability for planar vortex-pairs with prescribed impulse

G. R. Burton

Department of Mathematical Sciences

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

12 Citations (SciVal)

Abstract

Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the constraint set comprises the set of all equimeasurable rearrangements of a given function (representing vorticity) that have a prescribed impulse (linear momentum). A form of orbital stability is deduced.

Original language	English
Pages (from-to)	547-572
Number of pages	26
Journal	Journal of Differential Equations
Volume	270
Early online date	15 Sept 2020
DOIs	https://doi.org/10.1016/j.jde.2020.08.009
Publication status	Published - 5 Jan 2021

Keywords

Compactness
Convexity
Maximiser
Rearrangements
Stability
Vortex

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2020.08.009

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AB - Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the constraint set comprises the set of all equimeasurable rearrangements of a given function (representing vorticity) that have a prescribed impulse (linear momentum). A form of orbital stability is deduced.

KW - Compactness

KW - Convexity

KW - Maximiser

KW - Rearrangements

KW - Stability

KW - Vortex

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Compactness and stability for planar vortex-pairs with prescribed impulse

Abstract

Keywords

ASJC Scopus subject areas

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