Gluing Methods for Vortex Dynamics in Euler Flows

Juan Davila, Manuel Del Pino, Monica Musso, Juncheng Wei

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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 N moving 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 gluing approach for the construction of smooth N-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 desingularization. We succeed in applying those ideas in this highly challenging setting.

Original languageEnglish
Pages (from-to)1467-1530
Number of pages64
JournalArchive for Rational Mechanics and Analysis
Volume235
Issue number3
Early online date9 Sep 2019
DOIs
Publication statusPublished - 1 Mar 2020

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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