Journal of Mathematical Fluid Mechanics

, Volume 12, Issue 2, pp 202–242 | Cite as

An Eigenvalue Criterion for Stability of a Steady Navier–Stokes Flow in \({\mathbb{R}}^3\)

  • Paul Deuring
  • Jiří Neustupa
Article

Abstract.

We study the resolvent equation associated with a linear operator \({\mathcal{L}}\) arising from the linearized equation for perturbations of a steady Navier–Stokes flow \({\mathbf{U^*}}\). We derive estimates which, together with a stability criterion from [33], show that the stability of \({\mathbf{U^*}}\) (in the L2-norm) depends only on the position of the eigenvalues of \({\mathcal{L}}\), regardless the presence of the essential spectrum.

Mathematics Subject Classification (2000).

Primary 35Q30, 35B35 secondary 76D05, 76E09 

Keywords.

Navier–Stokes equations stability Oseen equation resolvent estimates 

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Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  • Paul Deuring
    • 1
  • Jiří Neustupa
    • 2
  1. 1.Laboratoire de MathématiquesUniversité du LittoralCalais cédexFrance
  2. 2.Czech Academy of SciencesMathematical InstitutePraha 1Czech Republic

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