Resolvent Estimates for a Perturbed Oseen Problem

  • Paul Deuring

Abstract

We consider a resolvent equation arising from a stability problem for exterior Navier-Stokes flows with nonzero velocity at infinity.

Keywords

Stability Oseen system resolvent estimate 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    K.I. Babenko, Spectrum of the linearized problem of flow of a viscous incompressible liquid round a body. Sov. Phys. Dokl. 27 (1982), 25–27.MATHGoogle Scholar
  2. [2]
    W. Borchers, T. Miyakawa, L 2-decay for Navier-Stokes flows in unbounded domains, with application to exterior stationary flows. Arch. Rat. Mech. Anal. 118 (1992), 273–295.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Deuring, The resolvent problem for the Stokes system in exterior domains: an elementary approach. Math. Methods Appl. Sci. 13 (1990), 335–349.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    P. Deuring, S. Kračmar, Exterior stationary Navier-Stokes flows in 3D with nonzero velocity at infinity: approximation by flows in bounded domains. Math. Nachr. 269–270 (2004), 86–115.CrossRefGoogle Scholar
  5. [5]
    P. Deuring, J. Neustupa, An eigenvalue criterion for stability of Navier-Stokes flows in3. Submitted.Google Scholar
  6. [6]
    G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I. Linearized steady problems (rev. ed.). Springer, 1998.Google Scholar
  7. [7]
    G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. II. Nonlinear steady problems. Springer, 1994.Google Scholar
  8. [8]
    G.P. Galdi, M. Padula, A new approach to energy theory in the stability of fluid motion. Arch. Rat. Mech. Anal. 110 (1990) 187–286.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    G.P. Galdi, S. Rionero, Weighted energy methods in fluid dynamics and elasticity. Lecture Notes in Mathematics 1134, Springer, 1985.Google Scholar
  10. [10]
    D. Henry, Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics 840, Springer, 1981.Google Scholar
  11. [11]
    P. Maremonti, Asymptotic stability theorems for viscous fluid motions in exterior domains. Rend. Sem. Mat. Univ. Padova 71 (1984), 35–72.MathSciNetMATHGoogle Scholar
  12. [12]
    K. Masuda, On the stability of incompressible viscous fluid motions past bodies. J. Math. Soc. Japan 27 (1975), 294–327.MATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    J. Neustupa, Stabilizing influence of a skew-symmetric operator in semilinear parabolic equations. Rend. Mat. Sem. Univ. Padova 102 (1999), 1–18.MathSciNetGoogle Scholar
  14. [14]
    J. Neustupa, Stability of a steady solution of a semilinear parabolic system in an exterior domain. Far East J. Appl. Math. 15 (2004), 309–331.MATHMathSciNetGoogle Scholar
  15. [15]
    J. Neustupa, Stability of a steady viscous incompressible flow past an obstacle. To appear in J. Math. Fluid Mech.Google Scholar
  16. [16]
    A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer, 1983.Google Scholar
  17. [17]
    Y. Shibata, On an exterior initial boundary value problem for Navier-Stokes equations. Quarterly Appl. Math. 57 (1999), 117–155.MATHMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Paul Deuring
    • 1
  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral “Côte d’Opale”Calais cédexFrance

Personalised recommendations