Contents Online
Dynamics of Partial Differential Equations
Volume 1 (2004)
Number 1
On spectrum of the linearized 3D Euler equation
Pages: 49 – 63
DOI: https://dx.doi.org/10.4310/DPDE.2004.v1.n1.a2
Authors
Abstract
We investigate essential spectrum of the Euler equation linearizedabout an arbitrary smooth steady flow in dimension 3. It is provedthat for every Lyapunov-Oseledets exponent $\m$ of the associatedbicharacteristic-amplitude system, the circle of radius $e^{\mut}$ has a common point with the spectrum. If, in addition, $\mu$is attained on an aperiodic point, then the spectrum contains theentire circle.
Keywords
linearized Euler equation, essential spectrum, Lyapunov-Oseledets exponents
2010 Mathematics Subject Classification
Primary 76E09. Secondary 34D09.
Published 1 January 2004