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.
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.
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Shvydkoy, Roman 1
@article{CRMATH_2010__348_15-16_897_0,
author = {Shvydkoy, Roman},
title = {Continuous spectrum of the {3D} {Euler} equation is a solid annulus},
journal = {Comptes Rendus. Math\'ematique},
pages = {897--900},
publisher = {Elsevier},
volume = {348},
number = {15-16},
year = {2010},
doi = {10.1016/j.crma.2010.07.009},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2010.07.009/}
}
TY - JOUR AU - Shvydkoy, Roman TI - Continuous spectrum of the 3D Euler equation is a solid annulus JO - Comptes Rendus. Mathématique PY - 2010 SP - 897 EP - 900 VL - 348 IS - 15-16 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2010.07.009/ DO - 10.1016/j.crma.2010.07.009 LA - en ID - CRMATH_2010__348_15-16_897_0 ER -
%0 Journal Article %A Shvydkoy, Roman %T Continuous spectrum of the 3D Euler equation is a solid annulus %J Comptes Rendus. Mathématique %D 2010 %P 897-900 %V 348 %N 15-16 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2010.07.009/ %R 10.1016/j.crma.2010.07.009 %G en %F CRMATH_2010__348_15-16_897_0
Shvydkoy, Roman. 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
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