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The L 2 Essential Spectrum of the 2D Euler Operator

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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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Authors and Affiliations

  1. Department of Mathematics, UNC Chapel Hill, Phillips Hall CB #3250, Chapel Hill, NC, 27599, USA

    Graham Cox

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  1. Graham Cox
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Correspondence to Graham Cox.

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Communicated by R. Shvydkoy

The author would like to thank Yuri Latushkin for many helpful discussions during the preparation of this work, and the referees for their comments and suggestions during the review process. This research has been supported by the Office of Naval Research under the MURI grant N00014-11-1-0087.

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Cox, G. The L 2 Essential Spectrum of the 2D Euler Operator. J. Math. Fluid Mech. 16, 419–429 (2014). https://doi.org/10.1007/s00021-014-0165-6

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  • DOI: https://doi.org/10.1007/s00021-014-0165-6

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