Vol. 308, No. 2, 2020

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Existence of steady multiple vortex patches to the vortex-wave system

Daomin Cao and Guodong Wang

Vol. 308 (2020), No. 2, 257–279
Abstract

We prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a certain variational problem for the vorticity and studying the asymptotic behavior as the vorticity strength goes to infinity.

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Keywords
vortex-wave system, vortex patch, Euler equations, Kirchhoff–Routh function, variational problem
Mathematical Subject Classification 2010
Primary: 35J50, 35Q35
Milestones
Received: 11 June 2018
Accepted: 10 July 2020
Published: 9 December 2020
Authors
Daomin Cao
Institute of Applied Mathematics
Chinese Academy of Sciences
Beijing,
China
Guodong Wang
Institute for Advanced Study in Mathematics
Harbin Institute of Technology
Harbin,
China