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Resolvent Estimates for a Perturbed Oseen Problem

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Abstract

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

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References

  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.

    MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Deuring, The resolvent problem for the Stokes system in exterior domains: an elementary approach. Math. Methods Appl. Sci. 13 (1990), 335–349.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  5. P. Deuring, J. Neustupa, An eigenvalue criterion for stability of Navier-Stokes flows in3. Submitted.

    Google Scholar 

  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. G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. II. Nonlinear steady problems. Springer, 1994.

    Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  9. G.P. Galdi, S. Rionero, Weighted energy methods in fluid dynamics and elasticity. Lecture Notes in Mathematics 1134, Springer, 1985.

    Google Scholar 

  10. D. Henry, Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics 840, Springer, 1981.

    Google Scholar 

  11. P. Maremonti, Asymptotic stability theorems for viscous fluid motions in exterior domains. Rend. Sem. Mat. Univ. Padova 71 (1984), 35–72.

    MathSciNet  MATH  Google Scholar 

  12. K. Masuda, On the stability of incompressible viscous fluid motions past bodies. J. Math. Soc. Japan 27 (1975), 294–327.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. Neustupa, Stabilizing influence of a skew-symmetric operator in semilinear parabolic equations. Rend. Mat. Sem. Univ. Padova 102 (1999), 1–18.

    MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  15. J. Neustupa, Stability of a steady viscous incompressible flow past an obstacle. To appear in J. Math. Fluid Mech.

    Google Scholar 

  16. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer, 1983.

    Google Scholar 

  17. Y. Shibata, On an exterior initial boundary value problem for Navier-Stokes equations. Quarterly Appl. Math. 57 (1999), 117–155.

    MATH  MathSciNet  Google Scholar 

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Deuring, P. (2007). Resolvent Estimates for a Perturbed Oseen Problem. In: Amann, H., Arendt, W., Hieber, M., Neubrander, F.M., Nicaise, S., von Below, J. (eds) Functional Analysis and Evolution Equations. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_11

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