Mathematical analysis/Partial differential equations
Quasi-periodic solutions for nonlinear wave equations
[Solutions quasi périodiques pour l'équation des ondes non linéaire]

Présenté par : Gilles Lebeau

Wang, Wei-Min1
1 CNRS and Department of Mathematics, Université Cergy-Pontoise, 95302 Cergy-Pontoise cedex, France
Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 601-604.

On construit des solutions quasi-périodiques en temps pour l'équation des ondes non linéaire sur le tore en dimension quelconque. Tous les résultats précédents se limitent au cercle. Cet article étend la méthode développée pour le cas limite elliptique dans [12] au cas hyperbolique. Le nouvel ingrédient est une propriété diophantienne des nombres algébriques.

We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This extends the method developed in the limit-elliptic setting in [12] to the hyperbolic setting. The additional ingredient is a Diophantine property of algebraic numbers.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.04.014
Wang, Wei-Min 1

1 CNRS and Department of Mathematics, Université Cergy-Pontoise, 95302 Cergy-Pontoise cedex, France 
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Wang, Wei-Min. Quasi-periodic solutions for nonlinear wave equations. Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 601-604. doi : 10.1016/j.crma.2015.04.014. http://www.numdam.org/articles/10.1016/j.crma.2015.04.014/

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