Recherche et téléchargement d’archives de revues mathématiques numérisées

 
 
  Table des matières de ce fascicule | Article précédent | Article suivant
Ma, Tian; Wang, Shouhong
Structural evolution of the Taylor vortices. ESAIM : Modélisation Mathématique et Analyse Numérique, 34 no. 2 (2000), p. 419-437
Texte intégral djvu | pdf | Analyses MR 1765668 | Zbl 0954.76018

URL stable: http://www.numdam.org/item?id=M2AN_2000__34_2_419_0

Bibliographie

[1] R. Abraham and J. Marsden, Foundations of Mechanics, Addison-Wesley: Reading, MA (1978).  MR 515141 |  Zbl 0393.70001
[2] D. V. Anosov and V. Arnold, Dynamical Systems I, Springer-Verlag, New York, Heidelberg, Berlin (1985).  MR 970793 |  Zbl 0658.00008
[3] V. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, Heidelberg, Berlin (1978).  MR 690288 |  Zbl 0386.70001
[4] Alain Bensoussan, Jacques-Louis Lions and Papanicolaou George, Asymptotic analysis for periodic structures, Ser. Studies in Mathematics and its Applications. 5; North-Holland Publishing Co., Amsterdam (1978) 700.  MR 503330 |  Zbl 0404.35001
[5] D. Chillingworth, Differential topology with a view to applications. Pitman, London, San Francisco, Melbourne. Research Notes in Mathematics, 9 (1976).  MR 646088 |  Zbl 0336.58001
[6] A. Chorin, Vorticity and Turbulence, Springer-Verlag (1994).  MR 1281384 |  Zbl 0795.76002
[7] P. Constantin and C. Foias, The Navier-Stokes Equations, Univ. of Chicago Press, Chicago (1988).  MR 972259 |  Zbl 0687.35071
[8] L. Caffarelli and R. Kohn and L. Nirenberg, On the regularity of the solutions of Navier-Stokes Equations. Comm. Pure Appl. Math. 35 (1982) 771-831.  MR 673830 |  Zbl 0509.35067
[9] Strebel, Kurt, Quadratic differentials, Springer-Verlag, Berlin (1984) 184.  MR 743423 |  Zbl 0547.30001
[10] A. Fathi, F. Laudenbach and V. Poénaru, Travaux de Thurston sur les surfaces. Asterisque 66-67 (1979).  MR 568308 |  Zbl 0446.57010
[11] A. Fannjiang and G. Papanicolaou, Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54 (1994) 333-408.  MR 1265233 |  Zbl 0796.76084
[12] H. Hopf, Abbildungsklassen in-dirnensionaler mannigfaltigkeiten. Math. Annalen 96 (1926) 225-250.  JFM 52.0571.01
[13] D. Gottlieb, Vector fields and classical theorems of topology. Rendiconti del Seminario Matematico e Fisico, Milano 60 (1990) 193-203.  MR 1229491 |  Zbl 0810.57020
[14] J. Milnor, Topology from the differentiable viewpoint. University Press of Virginia, based on notes by D.W. Weaver, Charlott-seville (1965).  MR 226651 |  Zbl 0136.20402
[15] J. Guckenheimer and P. J. Holmes, Nonlinear oscillations, dynamical Systems, and bifurcations of vector fields, Springer-Verlag, New York, Heidelberg, Berlin (1983).  MR 709768 |  Zbl 0515.34001
[16] J. K. Haie, Ordinary differential equations, Robert E. Krieger Publishing Company, Malabar, Florida (1969).  Zbl 0433.34003
[17] M. W. Hirsch, Differential topology, Springer-Verlag, New York, Heidelberg, Berlin (1976).  MR 448362 |  Zbl 0356.57001
[18] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris (1969).  MR 259693 |  Zbl 0189.40603
[19] A. Katok and B. Hasselblatt, Introduction to the Modem Theory of Dynamical Systems, Cambridge University Press (1995).  MR 1326374 |  Zbl 0878.58020
[20] J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que posent l'hydrodynamique. J. Math. Pures et Appl. XII (1933) 1-82.
Article |  Zbl 0006.16702
[21] J. L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of the atmosphere and applications. Nonlinearity 5 (1992) 237-288.  MR 1158375 |  Zbl 0746.76019
[22] J. L. Lions, R. Temam and S. Wang, On the Equations of Large-Scale Ocean. Nonlinearity 5 (1992) 1007-1053.  MR 1187737 |  Zbl 0766.35039
[23] J. L. Lions, R. Temam and S. Wang, Models of the coupled atmosphere and ocean (CAO I). Computational Mechanics Advance, 1 (1993) 3-54.  MR 1252502 |  Zbl 0805.76011
[24] J. L. Lions, R. Temam and S. Wang, Geostrophic Asymptotics of the Primitive Equations of the Atmosphere. Topological Methods in Nonlinear Analysis 4; note "Special issue dedicated to J. Leray" (1994) 253-287.  MR 1350974 |  Zbl 0846.35106
[25] J. L. Lions, R. Temam and S. Wang, Mathematical study of the coupled models of atmosphere and ocean (CAO III). J. Math. Pures Appl. 73 (1995) 105-163.  MR 1325825 |  Zbl 0866.76025
[26] J. L. Lions, R. Temam and S. Wang, A Simple Global Model for the General Circulation of the Atmosphere, "Dedicated to Peter D. Lax and Louis Nirenberg on the occasion of their 70th birthdays". Comm. Pure. Appl. Math. 50 (1997) 707-752.  MR 1454171 |  Zbl 0992.86001
[27] P. L. Lions, Mathematical Topics in Fluid Mechanics, Oxford science Publications (1996).  Zbl 0866.76002
[28] A. Majda, Vorticity and the mathematical theory of incompressible fluid flow. Frontiers of the mathematical sciences: 1985 (New York). Comm. Pure Appl. Math. 39 (1986) S187-S220.  MR 861488 |  Zbl 0595.76021
[29] T. Ma and S. Wang, Dynamics of Incompressible Vector Fields. Appl. Math. Lett. 12 (1999) 39-42.  MR 1750594 |  Zbl 0989.37012
[30] T. Ma and S. Wang, Dynamics of 2-D Incompressible Flows. Proceedings of the International Conferences on Differential Equations and Computation (1999).  MR 1774477 |  Zbl 0957.37046
[31] T. Ma and S. Wang, The Geometry of the Stream Lines of Steady States of the Navier-Stokes Equations. Contemporary Mathematics, AMS 238 (1999) 193-202.  MR 1724664 |  Zbl 0947.35110
[32] T. Ma and S. Wang, Block structure and stability of 2-D Incompressible Flows (in preparation, 1999).
[33] T. Ma and S. Wang, Structural classification and stability of divergence-free vector fields. Nonlinearity (revised, 1999).
[34] A. Majda, The interaction of nonlinear analysis and modern applied mathematics. Proc. Internat. Congress Math., Kyoto, 1990, Springer-Verlag, New York, Heidelberg, Berlin (1991) Vol. 1.  MR 1127159 |  Zbl 1153.76300
[35] N. Markley, The Poincaré-Bendixson theorem for Klein bottle. Trans. AMS 135 (1969).  MR 234442 |  Zbl 0175.50101
[36] L. Markus and R. Meyer, Generic Hamiltoman Systems are neither integrable nor ergodic. Memoirs of the American Mathematical Society 144 (1974).  Zbl 0291.58009
[37] J. Moser, Stable and Random Motions in Dynamical Systems. Ann. Math. Stud. No. 77 Princeton (1973).  MR 442980 |  Zbl 0271.70009
[38] J. Palis and W. de Melo, Geometric theory of dynamical Systems, Springer-Verlag, New York, Heidelberg, Berlin (1982).  MR 669541 |  Zbl 0491.58001
[39] J. Palis and S. Smale, Structural stability theorem. Global Analysis. Proc. Symp. in Pure Math. XIV (1970).  MR 267603 |  Zbl 0214.50702
[40] M. Peixoto, Structural stability on two dimensional manifolds. Topology 1 (1962) 101-120.  MR 142859 |  Zbl 0107.07103
[41] C. Pugh, The closing lemma. Amer. J. Math. 89 (1967) 956-1009.  MR 226669 |  Zbl 0167.21803
[42] Shub, Michael, Stabilité globale des systèmes dynamiques. Société Mathématique de France. Note With an English preface and summary Astérisque 56 (1978) iv+211.  MR 513592 |  Zbl 0396.58014
[43] C. Robinson, Generic properties of conservative systems, I, II. Amer. J. Math. 92 (1970) 562-603 and 897-906.  MR 273640 |  Zbl 0212.56601
[44] C. Robinson, Structure stability of vector fields. Ann. of Math. 99 (1974) 154-175.  MR 334283 |  Zbl 0275.58012
[45] C. Robinson, Structure stability of C1 diffeomorphisms. J. Differential Equations 22 (1976) 28-73.  MR 474411 |  Zbl 0343.58009
[46] G. Schwartz, Hodge decomposition-A method for solving boundary value problems. Lecture Notes in Mathematics 1607 Springer-Verlag (1995).  MR 1367287 |  Zbl 0828.58002
[47] S. Smale, Differential dynamical systems. Bull. AMS 73 (1967) 747-817.
Article |  MR 228014 |  Zbl 0202.55202
[48] F. Takens, Hamiltonian systems: generic properties of closed orbits and local perturbations. Math. Ann. 188 (1970) 304-312.  MR 284670 |  Zbl 0191.21602
[49] G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. A 223 (1923) 289-343.  JFM 49.0607.01
[50] R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, 3rd edition, North Holland, Amsterdam (1984).  MR 769654 |  Zbl 0568.35002
[51] R. Thom, Structural Stability and Morphogenesis, Benjamin-Addison Wesley (1975).  MR 488156 |  Zbl 0303.92002
[52] W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces. Bull. AMS 19 (1988) 417-431.
Article |  MR 956596 |  Zbl 0674.57008
[53] V. Trofimov, Introduction to Geometry on Manifolds with Symmetry, MIA Kluwer Academic Publishers (1994).  MR 1367288 |  Zbl 0804.53002
[54] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, Heidelberg, Berlin (1990).  MR 1056699 |  Zbl 0701.58001
[55] J. C. Yoccoz, Recent developments in dynamics, in Proc. Internat. Congress. Math., Zurich (1994), Birkhauser Verlag, Basel, Boston, Berlin (1994) 246-265 Vol. 1.  MR 1403926 |  Zbl 0844.58001
Copyright Cellule MathDoc 2014 | Crédit | Plan du site