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Tohoku Mathematical Journal
SECOND SERIES VOL. 62, NO. 2
|Tohoku Math. J.|
62 (2010), 287-309
SPECTRAL PROPERTIES IN $L^q$ OF AN OSEEN OPERATOR MODELLING FLUID FLOW PAST A ROTATING BODY
Reinhard Farwig and Jiří Neustupa
(Received April 20, 2009, revised February 1, 2010)
We study the spectrum of a linear Oseen-type operator which arises from equations of motion of a viscous incompressible fluid in the exterior of a rotating compact body. We prove that the essential spectrum consists of an infinite set of overlapping parabolic regions in the left half-plane of the complex plane. The full spectrum coincides with the essential and continuous spectrum if the operator is considered in the whole 3D space. Our approach is based on the Fourier transform in the whole space and the transfer of the results to the exterior domain.
2000 Mathematics Subject Classification.
Primary 35Q35; Secondary 35P99, 76D07.
Key words and phrases.
Eigenvalues, essential spectrum, modified Oseen problem, rotating obstacle.
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