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Relative Periodic Solutions of the N-Vortex Problem Via the Variational Method

Wang, Qun (2018), Relative Periodic Solutions of the N-Vortex Problem Via the Variational Method, Archive for Rational Mechanics and Analysis, 231, 3, p. 1401–1425. 10.1007/s00205-018-1300-y

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Type
Article accepté pour publication ou publié
Date
2018
Journal name
Archive for Rational Mechanics and Analysis
Volume
231
Number
3
Publisher
Springer
Pages
1401–1425
Publication identifier
Metadata
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Author(s)
Wang, Qun
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that there exist infinitely many normalised relative periodic orbits on a dense subset of all energy levels, which are neither fixed points nor relative equilibria.
Subjects / Keywords
N-Vortex; Variational Method