Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation

C. Foias; R. Temam

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1978)

  • Volume: 5, Issue: 1, page 29-63
  • ISSN: 0391-173X

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Foias, C., and Temam, R.. "Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.1 (1978): 29-63. <http://eudml.org/doc/83778>.

@article{Foias1978,
author = {Foias, C., Temam, R.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {fre},
number = {1},
pages = {29-63},
publisher = {Scuola normale superiore},
title = {Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation},
url = {http://eudml.org/doc/83778},
volume = {5},
year = {1978},
}

TY - JOUR
AU - Foias, C.
AU - Temam, R.
TI - Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1978
PB - Scuola normale superiore
VL - 5
IS - 1
SP - 29
EP - 63
LA - fre
UR - http://eudml.org/doc/83778
ER -

References

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  1. [1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, II, Comm. Pure Appl. Math., 12 (1959), pp. 623-727 et 17 (1964), pp. 35-92. Zbl0093.10401MR162050
  2. [2] F. Bruhat - H. Whitney, Quelques propriétés fondamentales des ensembles analytiques réels, Comm. Math. Helv., 33 (1959), pp. 132-160. Zbl0100.08101MR102094
  3. [3] H. Cartan, Séminaire de l'Ecole Normale Supérieure, 1951- 52 et 1953-54. 
  4. [4] L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova, 31 (1961), pp. 308-340. Zbl0116.18002MR138894
  5. [5] A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Annales Inst. Fourier, 16 (1966), pp. 1-95. Zbl0146.31103MR203082
  6. [6] G. Duvaut - J.L. Lions, Les inéquations variationnelles en Mécanique et en Physique, Dunod, Paris, 1972. Zbl0298.73001MR464857
  7. [7] C. Foias, Solutions statistiques des equations de Navier-Stokes, Cours au Collège de France, 1974. 
  8. [8] C. Foias - R. Temam, On the stationary statistical solutions of the Navier-Stokes equations and turbulence, Publication Mathématiqued'Orsay, n. 120-75-28, 1975. 
  9. [9] C. Foias - R. Temam, Structure of the set of stationary solutions of the Navier-Stokes equations, Comm. Pure Appl. Math., 30 (1977), pp. 149-164. Zbl0335.35077MR435626
  10. [10] M. Hervé, Several Complex Variables, Local Theory, Oxford Univ. Press and Tata Institute of Fundamental Research, 1963. Zbl0113.29003MR151632
  11. [11] E. Hopf, Abzweigung einer Periodischen Lösung eines Differentialsystems, Berichten der Math. Phys. Klasse der Sächsischen Akademie der Wissenschaften zu Leipzig, 94 (1942), pp. 1-22. 
  12. [12] E. Hopf, A mathematical example displaying features of turbulence, Comm. Pure Appl. Math., 1 (1948), pp. 303-322. Zbl0031.32901MR30113
  13. [13] E. Hopf, Repeated branching through loss of stability, an example, Proc. Conf. Diff. Equations, University of Maryland, 1955. Zbl0073.41603MR83087
  14. [14] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1969 Zbl0184.52603MR254401
  15. [15] P. Lailly, Thèse, Université de Paris-Sud, 1976. 
  16. [16] L. Landau, On the problem of turbulence, Doklady Akad. Nauk, USSR, 44 (1944), pp. 311-314. Zbl0063.03437MR11997
  17. [17] L. Landau - E.M. Lifshitz, Fluid Mechanics, London, Pergamon Press, 1959. Zbl0146.22405MR108121
  18. [18] O.E. Lanford, III, Bifurcation of periodic solutions into invariant Tori. : the work o f Ruelle and Takens, Lecture Notes in Math. n. 322, pp. 159-192, Springer-Verlga, 1973. Zbl0272.34039
  19. [19] J. Leray, Etude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique, J. Math. Pures Appl., 12 (1933), pp. 1-82. Zbl0006.16702JFM59.0402.01
  20. [20] J. Leray, Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J. Math. Pures Appl., 13 (1934), pp. 331-418. Zbl60.0727.01JFM60.0727.01
  21. [21] J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., 63 (1934), pp. 193-248. JFM60.0726.05
  22. [22] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  23. [23] J.L. Lions - E. Magenes, Non homogeneous boundary value problems and applications, Springer-Verlag, Heidelberg, New York, 1973. Zbl0223.35039MR350179
  24. [24] Gh. Minéa, Remarques sur l'unicité de la solution stationnaire d'une équation de type Navier-Stokes, Revue Roum. Math. Pures Appl., 21, no. 8 (1976), pp. 1071-1075. Zbl0365.76027MR433059
  25. [25] R. Narasimhan, Introduction to the theory of analytic spaces, Lecture Notes in Math., vol. 25, Springer-Verlag (1966). Zbl0168.06003MR217337
  26. [26] J Nečas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. MR227584
  27. [27] P. Rabinowitz, Existence and non uniqueness of rectangular solutions of the Bénard problem, Arch. Rat. Mech. Anal., 29 (1968), pp. 32-57. Zbl0164.28704MR233557
  28. [28] P. Rabinowitz, Editor, Proceeding on a Conference on Bifurcation Theory held at Madison, October 1976, Academic Press. 
  29. [29] G. De Rham, Variétés différentiables, Hermann, Paris, 1960. Zbl0089.08105
  30. [30] D. Ruelle - F. Takens, On the nature of turbulence, Comm. Math. Phys., 20 (1971), pp. 167-192 et 23 (1971), pp. 343-344. Zbl0227.76084MR284067
  31. [31] D. Sattinger, Topics in stability and bifurcation theory, Lecture Notes in Math., n. 309, Springer-Verlag, 1973. Zbl0248.35003MR463624
  32. [32] J.C. Saut, Exposé dans le séminaire d'Equations aux Dérivées Partielles non linéaires d'Orsay, 1975-76, Publication Mathématique d'Orsay, en cours de parution. 
  33. [33] R. Temam, Introduction à certains problèmes de valeurs propres non linéaires, Exposé de Séminaire rédigé par J. C. Saut, 1972. 
  34. [34] R. Temam, On the theory and numerical analysis of Navier-Stokes equations, Lecture Notes n. 9, 1973, Department of Mathematics, University of Maryland. Zbl0273.35002
  35. [35] R. Temam, Navier-Stokes equations, theory and numerical analysis, North-Holland, Amsterdam, 1977. Zbl0383.35057MR609732
  36. [36] R. Temam, Turbulence and Navier-Stokes equation, Proceeding of a Conference held at Orsay, Lecture Notes in Mathematics, vol. 565, Springer-Verlag, 1976. Zbl0336.00012MR438886
  37. [37] W. Velte, Stabilitäts und Vevrweigung stationärer Lösungen der Navier-Stokesschen Gleichungen beim Taylor problem, Arch. Rat. Mech. Anal., 22 (1966), pp. 1-14. Zbl0233.76054MR191226
  38. [38] W. Velte, Stabilitätsverhalten und Verweigung Stationärer Lôsungen der Navier-Stokesschen Gleichungen, Arch. Rat. Mech. Anal., 16 (1964), pp. 97-125. Zbl0131.41808MR182240
  39. [39] I.I. Vorovich - V.I. Yudovich, Stationary flows of incompressible viscous fluids, Mat. Sborn., 53 (1961), pp. 393-428. 

Citations in EuDML Documents

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  1. Atanda Boussari, Erich Maschke, Bernard Saramito, Steady tearing mode instabilities with a resistivity depending on a flux function
  2. H. Beirão Da Veiga, On the barotropic motion of compressible perfect fluids
  3. H. Beirão da Veiga, Viscous Incompressible Flows Under Stress-Free Boundary Conditions. The Smoothness Effect of Near Orthogonality
  4. R. V. Saraykar, N. E. Joshi, Structure of the set of stationary solutions of viscous hydromagnetic equations with diffusivity
  5. Tahar-Zamène Boulmezaoud, Yvon Maday, Tahar Amari, On the linear force-free fields in bounded and unbounded three-dimensional domains
  6. Pierangelo Marcati, Albert Milani, Fluid flow in macromolecular systems and related perturbation problems
  7. Nicolas Besse, Dietmar Kröner, Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system
  8. R. Temam, Qualitative Properties of Navier-Stokes Equations
  9. Paolo Secchi, Existence theorems for compressible viscous fluids having zero shear viscosity
  10. Elżbieta Motyl, Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations

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