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

2003/06/10 by Roman Shvidkoy, Shvidkoy, Roman, Yuri Latushkin +1
Mathematics · Physics and Astronomy · #37D25 #47B33 #47D99 #76E99 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:37D25 #msc:47B33 #msc:47D99 #msc:76E99

paper · pdf · doi:10.48550/arxiv.math-ph/0306027

6 pages

arxiv created 2003/06/10 · arxiv updated 2009/11/30

Abstract

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.

Related

• Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents
• The Spectrum of a linearized 2D Euler operator
• Small scale creation of the Lagrangian flow in 2d perfect fluids
• On 2D Euler Equations: III. A Line Model
• An Evans function for the linearised 2D Euler equations using Hill's determinant