Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents
Shvydkoy, Roman ; Latushkin, Yuri
arXiv, 0306026 / Harvested from arXiv
Text on arXiv
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
Publié le : 2003-06-10
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  76E99,  37D25,  47B33,  47D99 
@article{0306026,
     author = {Shvydkoy, Roman and Latushkin, Yuri},
     title = {Essential spectrum of the linearized 2D Euler equation and
  Lyapunov-Oseledets exponents},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306026}
}

Shvydkoy, Roman; Latushkin, Yuri. Essential spectrum of the linearized 2D Euler equation and
  Lyapunov-Oseledets exponents. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306026/