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On the spectrum of a Stokes-type operator arising from flow around a rotating body. (English) Zbl 1126.35050
Summary: We present the description of the spectrum of a linear perturbed Stokes-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 \(L^2_\sigma(\Omega)\) we prove that the essential spectrum consists of a set of equally spaced half lines parallel to the negative real half line in the complex plane. Our approach is based on a reduction to invariant closed subspaces of \(L^2_\sigma(\Omega)\) and on a Fourier series expansion with respect to an angular variable in a cylindrical coordinate system attached to the axis of rotation. Moreover, we show that the leading part of the operator is normal if and only if the body is axially symmetric about this axis.

35Q35 PDEs in connection with fluid mechanics
35P20 Asymptotic distributions of eigenvalues in context of PDEs
76D07 Stokes and related (Oseen, etc.) flows
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