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arXiv · 1310.0704

The $L^2$ essential spectrum of the 2D Euler operator

Graham Cox
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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.

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Graham Cox. 2014-10-16. The $L^2$ essential spectrum of the 2D Euler operator. https://doi.org/10.1007/s00021-014-0165-6

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