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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 897-900 (août 2010)
Doi : 10.1016/j.crma.2010.07.009
Received : 30 October 2009 ;  accepted : 15 July 2010
Continuous spectrum of the 3D Euler equation is a solid annulus
Le spectre continu de l'equation d'Euler 3D est un anneau
 

Roman Shvydkoy 1
Department of Mathematics, Statistics and Computer Science, 851 S. Morgan St., M/C 249, University of Illinois at Chicago, Chicago, IL 60607, United States 

Abstract

In this Note we give a description of the continuous spectrum of the linearized Euler equations in three dimensions. Namely, for all but countably many times  , the continuous spectrum of the evolution operator   is given by a solid annulus with radii   and  , where μ and M are the smallest and largest, respectively, Lyapunov exponents of the corresponding bicharacteristic-amplitude system of ODEs.

The full text of this article is available in PDF format.
Résumé

On donne dans cette Note une description du spectre continu de l'équation d'Euler linearisée en dimension 3. Précisément, pour presque tout  , le spectre continu de l'opérateur d'évolution   est constitué d'un anneau de rayons   et  , où μ et M sont, respectivement, le plus petit et le plus grand exposant de Lyapunov du système d'EDO bicaractéristique-amplitude associé.

The full text of this article is available in PDF format.
1  The work is partially supported by the US National Science Foundation Grant DMS-0907812.


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