Comptes Rendus
Partial Differential Equations
Continuous spectrum of the 3D Euler equation is a solid annulus
[Le spectre continu de l'equation d'Euler 3D est un anneau]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 897-900.

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

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 tR, the continuous spectrum of the evolution operator Gt is given by a solid annulus with radii etμ and etM, where μ and M are the smallest and largest, respectively, Lyapunov exponents of the corresponding bicharacteristic-amplitude system of ODEs.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.07.009

Roman Shvydkoy 1

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
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Roman Shvydkoy. Continuous spectrum of the 3D Euler equation is a solid annulus. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 897-900. doi : 10.1016/j.crma.2010.07.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.009/

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