On the spectrum of a Stokes-type operator arising from flow around a rotating body
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- 作者：Reinhard Farwig and Ji?¨ª Neustupa
- 关键词：Mathematics Subject Classification (2000) Primary 35Q35 ; Secondary 35P99 ; Secondary 76D07
- 刊名：manuscripta mathematica
- 出版年：2007
- 出版时间：April, 2007
- 年：2007
- 卷：122
- 期：4
- 页码：419-437
- 全文大小：233 KB
文摘
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 L2s(W)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 L2s(W)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.