Abstract.
We study the unstable spectrum of an equation that arises in geophysical fluid dynamics known as the surface quasi-geostrophic equation. In general the spectrum is the union of discrete eigenvalues and an essential spectrum. We demonstrate the existence of unstable eigenvalues in a particular example. We examine the spectra of the semigroup and the evolution operator. We exhibit the structure of these spectra for general flows and prove that a spectral mapping theorem holds. We observe that the spectral properties of the SQG equation are closely analogous to those of the two-dimensional Euler equation.
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Friedlander, S., Shvydkoy, R. The Unstable Spectrum of the Surface Quasi-Geostrophic Equation. J. math. fluid mech. 7 (Suppl 1), S81–S93 (2005). https://doi.org/10.1007/s00021-004-0129-3
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DOI: https://doi.org/10.1007/s00021-004-0129-3