Gluing methods for vortex dynamics in Euler flows
Analysis of PDEs
2019-10-02 v2
Abstract
A classical problem for the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. is that of finding regular solutions with highly concentrated vorticities around moving {\em vortices}. The formal dynamic law for such objects was first derived in the 19th century by Kirkhoff and Routh. In this paper we devise a {\em gluing approach} for the construction of smooth -vortex solutions. We capture in high precision the core of each vortex as a scaled finite mass solution of Liouville's equation plus small, more regular terms. Gluing methods have been a powerful tool in geometric constructions by {\em desingularization}. We succeed in applying those ideas in this highly challenging setting.
Cite
@article{arxiv.1803.00066,
title = {Gluing methods for vortex dynamics in Euler flows},
author = {Juan Davila and Manuel del Pino and Monica Musso and Juncheng Wei},
journal= {arXiv preprint arXiv:1803.00066},
year = {2019}
}