Abstract.
We present the description of the spectrum of a linear perturbed Oseen-type operator which arises from equations of motion of a viscous incompressible fluid in the exterior of a rotating compact body. Considering the operator in the function space L 2 σ(Ω) we prove that the essential spectrum consists of an infinite set of overlapping parabolic regions in the left half-plane of the complex plane. Our approach is based on a reduction to invariant closed subspaces of L 2 σ(Ω) and on a Fourier series expansion with respect to an angular variable in a cylindrical coordinate system attached to the axis of rotation.
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Farwig, R., Neustupa, J. On the Spectrum of an Oseen-Type Operator Arising from Flow past a Rotating Body. Integr. equ. oper. theory 62, 169–189 (2008). https://doi.org/10.1007/s00020-008-1616-3
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DOI: https://doi.org/10.1007/s00020-008-1616-3