English

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

R2 v1 2026-06-22T01:39:02.099Z