Journal of Mathematical Fluid Mechanics

, Volume 16, Issue 3, pp 419–429 | Cite as

The L 2 Essential Spectrum of the 2D Euler Operator

  • Graham CoxEmail author


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.

Mathematics Subject Classification (2010)

Primary 76B99 Secondary 35Q31 


Euler equation essential spectrum Coarea formula 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsUNC Chapel HillChapel HillUSA

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