The Essential Spectrum of the Linearized 2D Euler Operator is a Vertical Band

Details The Essential Spectrum of the Linearized 2D Euler Operator is a Vertical Band The Essential Spectrum of the Linearized 2D Euler Operator is a Vertical Band

2003-06-10

arxiv.org/abs/math-ph/0306027v1

Physics

Mathematical Physics

6 pages

Scientific paper

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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