On the spectrum of a Stokes-type operator arising from flow around a rotating body
On the spectrum of a Stokes-type operator arising from flow around a rotating body
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关于旋转体周围流动产生的斯托克斯算子的谱
DOI：
10.1007/s00229-007-0078-2
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发表时间：
2007
影响因子：
0.6
通讯作者：
J. Neustupa
中科院分区：
文献类型：
--
作者：
R. Farwig;J. Neustupa
我们提出了线性扰动斯托克斯型算子的谱的描述，该算子由旋转紧凑体外部的粘性不可压缩流体的运动方程产生。考虑函数空间 $$L^2_{\sigma}(\Omega)$$ 中的算子，我们证明基本谱由一组等距的半线组成，这些半线平行于复平面中的负实半线。我们的方法基于 $$L^2_{\sigma}(\Omega)$$ 的不变闭子空间的简化以及关于附加到旋转轴的圆柱坐标系中的角度变量的傅里叶级数展开。此外，我们表明，当且仅当身体关于该轴轴对称时，算子的前导部分是正常的。
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.