The Spectrum of a Linearized 2D Euler Operator
نویسندگان
چکیده
منابع مشابه
The Essential Spectrum of the Linearized 2d Euler Operator Is a Vertical Band
We prove that the essential spectrum of the operator obtained by linearization about a steady state of the Euler equations governing the motion of inviscid ideal fluid in dimension two is a vertical strip whose width is determined by the maximal Lyapunov exponent of the flow induced by the steady state.
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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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ژورنال
عنوان ژورنال: Studies in Applied Mathematics
سال: 2004
ISSN: 0022-2526,1467-9590
DOI: 10.1111/j.0022-2526.2004.01510.x