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arXiv · 1010.4756

Continuous spectrum of the 3D Euler equation is a solid annulus

Roman Shvydkoy
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Abstract

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 $t\in \R$, the continuous spectrum of the evolution operator $G_t$ is given by a solid annulus with radii $e^{tμ}$ and $e^{t M}$, where $μ$ and $M$ are the smallest and largest, respectively, Lyapunov exponents of the corresponding bicharacteristic-amplitude system of ODEs.

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Roman Shvydkoy. 2010-10-22. Continuous spectrum of the 3D Euler equation is a solid annulus. https://arxiv.org/abs/1010.4756

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