Steady asymmetric vortex pairs for Euler equations

Zineb Hassainia, Taoufik Hmidi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.

Original languageEnglish (US)
Pages (from-to)1939-1969
Number of pages31
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number4
DOIs
StatePublished - Apr 2021

Keywords

  • Desingularization
  • Euler equations
  • Implicit function theorem
  • Steady vortex pairs
  • Vortex dynamics

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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