English

On concentrated traveling vortex pairs with prescribed impulse

Analysis of PDEs 2022-06-29 v2

Abstract

In this paper, we consider a constrained maximization problem related to planar vortex pairs with prescribed impulse. We prove existence, stability and asymptotic behavior for the maximizers, hence obtain a family of stable traveling vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. As a corollary, we get fine asymptotic estimates for Burton's vortex pairs with large impulse. For the non-concentrated case, we prove a form of stability for the Chaplygin-Lamb dipole.

Keywords

Cite

@article{arxiv.2205.13706,
  title  = {On concentrated traveling vortex pairs with prescribed impulse},
  author = {Guodong Wang},
  journal= {arXiv preprint arXiv:2205.13706},
  year   = {2022}
}

Comments

vorticity was assumed to be in $L^p$, $p>2$, and stability of Chaplygin-Lamb dipole was added