Spectral analysis of a Stokes-type operator arising from flow around a rotating body

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概要

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• We consider the spectrum of the Stokes operator with and without rotation effect for the whole space and exterior domains in Lq-spaces. Based on similar results for the Dirichlet-Laplacian on Rn, 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.

著者

• Farwig Reinhard

  Fachbereich Mathematik, Technische Universitat Darmstadt

• Neustupa Jiri

  Mathematical Institute, Czech Academy of Sciences

• Necasova Sarka

  Mathematical Institute of the Academy of Sciences of the Czech Republic

• Neasová Šárka

  Mathematical Institute, Czech Academy of Sciences

• Neustupa Jií

  Mathematical Institute, Czech Academy of Sciences

関連論文

• Spectral properties in $L^q$ of an Oseen operator modelling fluid flow past a rotating body
• Anisotropic L2-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body
• Spectral analysis of a Stokes-type operator arising from flow around a rotating body
• Anisotropic L^2-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body
• Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data
• On the Essential Spectrum of a Stokes-Type Operator Arising from Flow around a Rotating Body in the $L^q$-Framework(Kyoto Conference on the Navier-Stokes Equations and their Applications)

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