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An analytical and
numerical study of steady patches in the disc
Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi and Joan Mateu |
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Vol. 9 (2016), No. 7, 1609–1670
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DOI: 10.2140/apde.2016.9.1609
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Abstract |
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We prove the existence of -fold rotating patches for the Euler equations in the disc, for the simply connected and doubly connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the lowest symmetries and . We also discuss some numerical experiments highlighting the interaction between the boundary of the patch and the rigid one. |
Keywords
Euler equations, $V$-states, bifurcation
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Mathematical Subject Classification 2010
Primary: 35Q35, 37G40, 35Q31
Secondary: 76B47
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Milestones
Received: 20 October 2015
Revised: 27 April 2016
Accepted: 28 May 2016
Published: 7 November 2016
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Authors |
| Francisco de la Hoz | |
| Department of Applied Mathematics
and Statistics and Operations Research Faculty of Science and Technology University of the Basque Country UPV/EHU Barrio Sarriena S/N 48940 Leioa Spain |
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| Zineb Hassainia | |
| Courant Institute for Mathematical
Sciences New York University New York, NY 10012-1185 United States |
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| Taoufik Hmidi | |
| Institut de Recherche Mathématique
de Rennes Université de Rennes 1 Campus de Beaulieu 35 042 Rennes CEDEX France |
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| Joan Mateu | |
| Departament de Matemàtiques Universitat Autònoma de Barcelona 08193 Barcelona Spain |
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