Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents

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dc.creatorShvydkoy, Roman
dc.creatorLatushkin, Yuri
dc.date2003-06-10
dc.date.accessioned2026-07-07T04:30:15Z
dc.date.available2026-07-07T04:30:15Z
dc.descriptionThe linear stability of a steady state solution of 2D Euler equations of an ideal fluid is being studied. We give an explicit geometric construction of approximate eigenfunctions for the linearized Euler operator $L$ in vorticity form acting on Sobolev spaces on two dimensional torus. We show that each nonzero Lyapunov-Oseledets exponent for the flow induced by the steady state contributes a vertical line to the essential spectrum of $L$. Also, we compute the spectral and growth bounds for the group generated by $L$ via the maximal Lyapunov-Oseledets exponent. When the flow has arbitrarily long orbits, we show that the essential spectrum of $L$ on $L_2$ is the imaginary
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0306026
dc.identifierhttp://arxiv.org/abs/math-ph/0306026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57411
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject76E99; 37D25; 47B33; 47D99
dc.titleEssential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents
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