Compactness and stability for planar vortex-pairs with prescribed impulse
Analysis of PDEs
2020-02-28 v1 Functional Analysis
Optimization and Control
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 prescribed impulse (lnear momentum). A form of orbital stability is deduced.
Cite
@article{arxiv.2002.12260,
title = {Compactness and stability for planar vortex-pairs with prescribed impulse},
author = {G. R. Burton},
journal= {arXiv preprint arXiv:2002.12260},
year = {2020}
}