The $L^2$ essential spectrum of the 2D Euler operator
Analysis of PDEs
2014-10-17 v2
Abstract
Even in two dimensions, the spectrum of the linearized Euler operator is notoriously hard to compute. In this paper we give a new geometric calculation of the essential spectrum for 2D flows. This generalizes existing results---which are only available when the flow has arbitrarily long periodic orbits---and clarifies the role of individual streamlines in generating essential spectra.
Keywords
Cite
@article{arxiv.1310.0704,
title = {The $L^2$ essential spectrum of the 2D Euler operator},
author = {Graham Cox},
journal= {arXiv preprint arXiv:1310.0704},
year = {2014}
}
Comments
14 pages; hypotheses of the main theorem clarified