Tohoku Mathematical Journal

Spectral properties in $L^q$ of an Oseen operator modelling fluid flow past a rotating body

Reinhard Farwig and Jiří Neustupa

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Abstract

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.

Article information

Source
Tohoku Math. J. (2), Volume 62, Number 2 (2010), 287-309.

Dates
First available in Project Euclid: 23 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1277298650

Digital Object Identifier
doi:10.2748/tmj/1277298650

Mathematical Reviews number (MathSciNet)
MR2663458

Zentralblatt MATH identifier
1194.35324

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35P99: None of the above, but in this section 76D07: Stokes and related (Oseen, etc.) flows

Keywords
Eigenvalues essential spectrum modified Oseen problem rotating obstacle

Citation

Farwig, Reinhard; Neustupa, Jiří. Spectral properties in $L^q$ of an Oseen operator modelling fluid flow past a rotating body. Tohoku Math. J. (2) 62 (2010), no. 2, 287--309. doi:10.2748/tmj/1277298650. https://projecteuclid.org/euclid.tmj/1277298650


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