Spectral analysis of a Stokes-type operator arising from flow around a rotating body

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We consider the spectrum of the Stokes operator with and without rotation effect for the whole space and exterior domains in Lq-spaces. Based on similar results for the Dirichlet-Laplacian on Rn, n ≥ 2, we prove in the whole space case that the spectrum as a set in C does not change with q ∈ (1,∞), but it changes its type from the residual to the continuous or to the point spectrum with q. The results for exterior domains are less complete, but the spectrum of the Stokes operator with rotation mainly is an essential one, consisting of infinitely many equidistant parallel half-lines in the left complex half-plane. The tools are strongly based on Fourier analysis in the whole space case and on stability properties of the essential spectrum for exterior domains.

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