Bifurcation of rotating patches from Kirchhoff vortices

Taoufik  Hmidi; Joan  Mateu

doi:10.3934/dcds.2016038

Article Contents

2016, Volume 36, Issue 10: 5401-5422. Doi: 10.3934/dcds.2016038

This issue Previous Article On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation Next Article Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type

Bifurcation of rotating patches from Kirchhoff vortices

Taoufik Hmidi^1, and
Joan Mateu^2,

1.
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042 Rennes cedex
2.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia

Received: August 31, 2015

Revised: March 31, 2016

Published: May 2017

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Abstract

In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to Hölderian class.

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Mathematics Subject Classification: Primary: 35Q31; Secondary: 35Q35, 76B03.

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