Exact periodic traveling water waves with vorticity

Adrian Constantin; Walter Strauss

doi:10.1016/S1631-073X(02)02565-7

Exact periodic traveling water waves with vorticity
[Ondes d'eau avec tourbillons]

Adrian Constantin ¹ ; Walter Strauss ²

¹ Department of Mathematics, Lund University, PO Box 118, 22100 Lund, Sweden
² Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI 02912, USA

Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 797-800.

Résumé
Abstract

Pour le problème classique des ondes d'eau sans viscosité sous l'influence de la gravité, décrit par l'équation d'Euler avec une surface libre à fond plat, nous construisons des houles aux tourbillons. Ce sont des ondes symmétriques dont les profils sont monotones entre chaque sommet et creux. Nous employons la théorie de la bifurcation globale pour construire un ensemble connexe de telles solutions. Cet ensemble contient des ondes au profil non-oscillatoire et aussi des ondes qui approchent des flots avec des points de stagnation.

For the classical inviscid water wave problem under the influence of gravity, described by the Euler equation with a free surface over a flat bottom, we construct periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use global bifurcation theory to construct a connected set of such solutions. This set contains flat waves as well as waves that approach flows with stagnation points.

Reçu le : 2002-06-18
Accepté le : 2002-09-13
Publié le : 2002-10-05

DOI : 10.1016/S1631-073X(02)02565-7

Affiliations des auteurs :

Adrian Constantin ¹ ; Walter Strauss ²

¹ Department of Mathematics, Lund University, PO Box 118, 22100 Lund, Sweden
² Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI 02912, USA

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     author = {Adrian Constantin and Walter Strauss},
     title = {Exact periodic traveling water waves with vorticity},
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     language = {en},
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Adrian Constantin; Walter Strauss. Exact periodic traveling water waves with vorticity. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 797-800. doi : 10.1016/S1631-073X(02)02565-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02565-7/

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