Quasi-periodic solutions of the 2D Euler equation

Article type: Research Article

Authors: Crouseilles, Nicolas | Faou, Erwan^;

Affiliations: INRIA – Rennes Bretagne Atlantique, IPSO Project and IRMAR (University of Rennes 1), 35042 Rennes, France. E-mails: {Nicolas.Crouseilles, Erwan.Faou}@inria.fr

Note: [] Corresponding author.

Abstract: We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state depending on only one variable. The direction of propagation is orthogonal to this variable, and the support is concentrated on flat strips of the stationary state. The frequencies of the solution are given by the locally constant velocities associated with the stationary state.

Keywords: Euler equation, quasi-periodic solutions

DOI: 10.3233/ASY-2012-1117

Journal: Asymptotic Analysis, vol. 81, no. 1, pp. 31-34, 2013