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A survey on the functional dynamical system generated by the Navier-Stokes equations

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Approximation Methods for Navier-Stokes Problems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 771))

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References

  1. H. Federer, Geometric measure theory, Springer (New York, 1969).

    MATH  Google Scholar 

  2. C. Foias, Solutions statistiques des équations de Navier-Stokes, Cours au Collège de France (1974).

    Google Scholar 

  3. C. Foias-R. Temam, Structure of the set of stationary solutions of the Navier-Stokes equations,Comm. Pure Appl. Math.,30 (1977), 149–164.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Foias-R. Temam, Remarques sur les équations de Navier-Stokes stationnaires et les problèmes succesifs de bifurcation,Ann. Sc. Norm. Sup. Pisa,(IV)5(1978),29–63.

    MathSciNet  MATH  Google Scholar 

  5. C. Foias-R. Temam, Some analytic and geometric properties of the evolution Navier-Stokes equations, Journ. Math. Pures Appl., 58 (1979),339–368.

    MathSciNet  MATH  Google Scholar 

  6. C. Foias-R. Temam, Sur certaines propriétés génériques des équations de Navier-Stokes,Orsay(1974); to appear.

    Google Scholar 

  7. E. Hopf, A mathematical example displaying feature of turbulence, Comm. Pure Appl. Math., 1(1948),303–322.

    Article  MathSciNet  MATH  Google Scholar 

  8. E. Hopf, Abzweigung einer periodischen Lösung eines Differentialsystems, Berichten Math.-Phys. Kl. Wiss. Leipzig,94(1942),1–22.

    Google Scholar 

  9. G. Iooss, Direct bifurcation of a steady solution of the Navier-Stokes equations into an invariant torus,Turbulence and Navier-Stokes equations, Orsay(1975),Lecture Notes in Math.,No565, Springer(1976),69–84.

    Google Scholar 

  10. V.I. Iudovich, Secondary flows and fluid instability between rotating cylinders,Prikl. Mat. Meh.,30(1966),688–698.

    MathSciNet  Google Scholar 

  11. D.D. Joseph, Stability of fluid motions. (I&II), Springer(Berlin, 1976).

    MATH  Google Scholar 

  12. J.P. Kahane, Mesures et dimensions,Turbulence and Navier-Stokes equations,Orsey(1975),Lecture Notes in Math.,No565,Springer (1976),94–103.

    Google Scholar 

  13. K. Kirchgässner, Bifurcation in nonlinear hydrodynamic stability, SIAM Rev., 17(1975),662–683.

    Article  MathSciNet  MATH  Google Scholar 

  14. K. Kirchgassner-P. Sorger, Branching analysis for the Taylor problem,Quart. J. Mech. Appl. Anal.,32(1969),183–209.

    Article  MathSciNet  MATH  Google Scholar 

  15. O.A. Ladyzenskaya, The mathematical theory of Viscous incompressible fluids,Gordon-Breach(New York,1963).

    Google Scholar 

  16. L.D. Landau-E.M. Lifshitz, Fluid Mechanics, Pergamon(Oxford,1959).

    MATH  Google Scholar 

  17. J. Leray, Sur le mouvement d'un liquide visqueux emlissant l'espace,Acta Math.,63(1934),193–249.

    Article  MathSciNet  Google Scholar 

  18. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires,Dunod (Paris,1969).

    MATH  Google Scholar 

  19. J.L. Lions-G. Prodi, Un théorème d'existence et unicité dans les équations de Navier-Stokes en dimension 2,C.R. Acad. Sci. Paris, 248(1959),3519–3521.

    MathSciNet  MATH  Google Scholar 

  20. E.N. Lorenz, Deterministic nonperiodic flows,Journ. Atmos. Sci., 20(1963),130–141.

    Article  Google Scholar 

  21. J. Mallet-Paret, Negatively invariant sets of compact maps and an extension of a theorem of Cartwright,Journ. Diff. Eq.,22(1976), 331–348.

    Article  MathSciNet  MATH  Google Scholar 

  22. B. Mandelbrot, Inermittent turbulence and fractal kurtosis and the spectral exponent 5/3+D,Turbulence and the Navier-Stokes equations, Orsay(1975),Lecture Notes in Math.,No565,Springer(1976),121–145.

    Google Scholar 

  23. G. Métivier, Etude asymptotique des valeurs propres et de la fonction spectrale de problèmes aux limites,Thèse,Univ. de Nice(1976).

    Google Scholar 

  24. G. Minea, Remarques sur l'unicité de la solution d'une équation de type Navier-Stokes,Revue Roum. Math. P. Appl.,21(1976),1071–1075.

    MathSciNet  MATH  Google Scholar 

  25. P.H. Rabinowitz, Existence and nonuniqueness of rectangular solutions of the Bénard problem,Arch. Rat. Mech. Anal.,29(1968),32–57.

    Article  MathSciNet  MATH  Google Scholar 

  26. D. Ruelle, Turbulence and Axiome A attractor,Proc. Intern. School math. Phys.,Univ. di Camerino(1974),162–181.

    Google Scholar 

  27. D. Ruelle, A Lorenz attractor and the problem of turbulence,Turbulence and Navier-Stokes equations,Orsay(1975),No565,Springer (1976),146–158.

    Google Scholar 

  28. D. Ruelle-F. Takens, On the nature of turbulence,Comm. Math. Phys.,20(1971),167–192;23(1971),343–344.

    Article  MathSciNet  MATH  Google Scholar 

  29. J.C. Saut-R. Temam, Propriétés de l'ensemble des solutions stationnaires ou périodiques des équations de Navier-Stokes,C.R. Acad. Sci. Paris,248(1977),A,673–676; Generic properties of the Navier-Stokes equations,Orsay(1979).

    MathSciNet  MATH  Google Scholar 

  30. V. Sheffer, Turbulence and Hausdorff dimension,Turbulence and Navier-Stokes equations,Orsay(1975),Lecture Notes in Math.,No565, Springer(1976),174–183.

    Google Scholar 

  31. R. Temam, Navier-Stokes equations.Theory and numerical analysis, North-Holland(New York,1977).

    Google Scholar 

  32. R. Temam, Une propriété générique de l'ensemble des solutions stationnaires ou périodiques des équations de Navier-Stokes,Funct. Anal. and Numerical Anal.,Japan-France Seminar,Tokyo-Kyoto(1976), Japan Soc. for the Prom. of Sci. (1978),483–493.

    Google Scholar 

  33. W. Velte, Stabilität und Verzweigung stationäre Lösungen des Navier-Stokes Gleichungen beim Taylor Problem,Arch. Rat. Mech. Anal., 22(1966),1–14.

    Article  MathSciNet  MATH  Google Scholar 

  34. R.F. Williams, The structure of the Lorenz attractors,Turbulence Seminar,Berkeley(1976/77),Lecture Notes in Math.,No615,Springer (1977),94–112.

    Google Scholar 

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Authors and Affiliations

  1. Université de Paris-Sud, 91405, Orsay, France

    C. Foias

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  1. C. Foias
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Reimund Rautmann

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© 1980 Springer-Verlag

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Foias, C. (1980). A survey on the functional dynamical system generated by the Navier-Stokes equations. In: Rautmann, R. (eds) Approximation Methods for Navier-Stokes Problems. Lecture Notes in Mathematics, vol 771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086907

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  • DOI: https://doi.org/10.1007/BFb0086907

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09734-1

  • Online ISBN: 978-3-540-38550-9

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