Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Essential spectrum of the linearized 2D Euler equation and
  Lyapunov-Oseledets exponents   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 vertical line to the essential spectrum of $L$. Also, we compute
the spectral and growth bounds for the group generated by $L$ via the maximal
Lyapunov-Oseledets exponent. When the flow has arbitrarily long orbits, we show
that the essential spectrum of $L$ on $L_2$ is the imaginary

26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph