JournalsaihpcVol. 25, No. 4pp. 713–724

The unstable spectrum of the Navier–Stokes operator in the limit of vanishing viscosity

  • Roman Shvydkoy

    Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, (M/C 249), Chicago, IL 60607, USA

  • Susan Friedlander

    Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, (M/C 249), Chicago, IL 60607, USA
The unstable spectrum of the Navier–Stokes operator in the limit of vanishing viscosity cover
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Abstract

The Navier–Stokes equations for the motion of an incompressible fluid in three dimensions are considered. A partition of the evolution operator into high frequency and low frequency parts is derived. This decomposition is used to prove that the eigenvalues of the Navier–Stokes operator in the inviscid limit converge precisely to the eigenvalues of the Euler operator beyond the essential spectrum.

Cite this article

Roman Shvydkoy, Susan Friedlander, The unstable spectrum of the Navier–Stokes operator in the limit of vanishing viscosity. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 4, pp. 713–724

DOI 10.1016/J.ANIHPC.2007.05.004