Essential Spectrum of the Linearized 2D Euler Equation and Lyapunov–Oseledets Exponents
نویسندگان
چکیده
منابع مشابه
Essential Spectrum of the Linearized 2D Euler Equation and Lyapunov–Oseledets Exponents
The 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 vert...
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In this note we continue the work in [SL], and give a full description of the essential spectrum for the linearized Euler operator L in dimension two. We prove that the essential spectrum of the operator is one solid vertical strip symmetric with respect to the imaginary axis. The width of the strip is determined by the maximal Lyapunov exponent Λ for the flow induced by the steady state. For c...
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ژورنال
عنوان ژورنال: Journal of Mathematical Fluid Mechanics
سال: 2005
ISSN: 1422-6928,1422-6952
DOI: 10.1007/s00021-004-0114-x