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首页> 外文期刊>Journal of the Mathematical Society of Japan >Spectral analysis of a Stokes-type operator arising from flow around a rotating body
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Spectral analysis of a Stokes-type operator arising from flow around a rotating body

机译：旋转体周围流动引起的斯托克斯型算子的光谱分析

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摘要

We consider the spectrum of the Stokes operator with and without rotation effect for the whole space and exterior domains in L~q-spaces. Based on similar results for the Dirichlet-Laplacian on R~n, n ≥ 2, we prove in the whole space case that the spectrum as a set in C does not change with q ∈(1,∞), but it changes its type from the residual to the continuous or to the point spectrum with q. The results for exterior domains are less complete, but the spectrum of the Stokes operator with rotation mainly is an essential one, consisting of infinitely many equidistant parallel half-lines in the left complex half-plane. The tools are strongly based on Fourier analysis in the whole space case and on stability properties of the essential spectrum for exterior domains.
机译：我们考虑L〜q空间中整个空间和外部域在有或没有旋转效应的情况下斯托克斯算子的谱。基于R〜n，n≥2上的Dirichlet-Laplacian的相似结果，我们证明了在整个空间情况下，C中的频谱集不会随q∈（1，∞）改变，而是会改变其类型从残差到连续或到点频谱外部域的结果不太完整，但是带旋转的Stokes算子的谱主要是必不可少的，它由左复半平面中的无限多等距平行半线组成。这些工具强烈地基于整个空间情况下的傅立叶分析，以及外部域基本光谱的稳定性。

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