Linearization and normal form of the Navier-Stokes equations with potential forces

Foias, C.; Saut, J. C.

Foias, C. ; Saut, J. C.

Annales de l'I.H.P. Analyse non linéaire, Tome 4 (1987) no. 1, pp. 1-47.

MR Zbl | 4 citations dans Numdam

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     author = {Foias, C. and Saut, J. C.},
     title = {Linearization and normal form of the {Navier-Stokes} equations with potential forces},
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     pages = {1--47},
     publisher = {Gauthier-Villars},
     volume = {4},
     number = {1},
     year = {1987},
     mrnumber = {877990},
     zbl = {0635.35075},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1987__4_1_1_0/}
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Foias, C.; Saut, J. C. Linearization and normal form of the Navier-Stokes equations with potential forces. Annales de l'I.H.P. Analyse non linéaire, Tome 4 (1987) no. 1, pp. 1-47. http://www.numdam.org/item/AIHPC_1987__4_1_1_0/

Bibliographie
Cité par

[1] V. Arnold, Geometrical methods in the theory of ordinary differential equations, Springer-Verlag. New York, 1983. | MR | Zbl

[2] M.S. Berger, P.T. Church, J.G. Timourian, Integrability of nonlinear differential equations via functional analysis, Proc. Symp. Pure Math., t. 45, 1986, Part I, p. 117- 123. | MR | Zbl

[3] N. Bourbaki, Variétés différentiables et analytiques, Fascicule de résultats, §1-7, Hermann, Paris, 1967. | MR | Zbl

[4] L. Cattabriga, Su un problema al contorno relativo al sistema di equazione di Stokes,Rend. Mat. Sem. Univ. Padova, t. 31, 1961, p. 308-340. | Numdam | MR | Zbl

[5] P. Constantin, C. Foias, Global Lyapunov exponents, Kaplan Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations, Comm. Pure Appl. Math., t. XXXVII, 1985, p. 1-28. | MR | Zbl

[6] C. Foias, Solutions statistiques des équations de Navier-Stokes, Cours au Collège de France, 1974.

[7] C. Foias, J.C. Saut, Asymptotic behavior, as t → + ∞ of solutions of Navier -Stokes equations and nonlinear spectral manifolds, Indiana Univ. Math. J., t. 33, 3, 1984, p. 459-471. | MR | Zbl

[8] C. Foias, J.C. Saut, On the smoothness of the nonlinear spectral manifolds of Navier -Stokes equations, Indiana Univ. Math. J., t. 33, 6, 1984, p. 911-926. | MR | Zbl

[9] C. Foias, J.C. Saut, Transformation fonctionnelle linéarisant les équations de Navier- Stokes, C. R. Acad. Sci. Paris, Série I, Math., t. 295, 1982, p. 325-327. | MR | Zbl

[10] C. Foias, J.C. Saut, Remarks on the spectrum of some self-adjoint operators, in preparation.

[11] C. Gardner, J. Greene, M. Kruskal, R. Miura, Korteweg de Vries equations, VI: Methods for exact solution, Comm. Pure Appl. Math., t. 27, 1974, p. 97-133. | MR | Zbl

[12] J.M. Ghidaglia, Long time behavior of solutions of abstract inequalities. Application to thermohydraulic and M. H. D. equations. J. Diff. Eq., t. 61, 2, 1986, p. 268-294. | MR | Zbl

[13] C. Guillope, Remarques à propos du comportement lorsque t → ∞, des solutions des équations de Navier-Stokes associées à une force nulle, Bull. Soc. Math. France, t. 111, 1983, p. 151-180. | Numdam | MR | Zbl

[14] E. Hopf, The partial differential equation ut + uux = μuxx, Comm. Pure Appl. Math., t. 3, 1950, p. 201-230. | Zbl

[15] G. Minea, Remarques sur l'unicité de la solution stationnaire d'une équation de type Navier-Stokes, Revue Roumaine Math. Pures Appl., t. 21, 1976, p. 1071-1075. | MR | Zbl

[16] N.V. Nikolenko, Complete integrability of the nonlinear Schrödinger equation, Soviet Math. Dokl., t. 17, 2, 1976, p. 398-402. | MR | Zbl

[17] N.V. Nikolenko, On the complete integrability of the nonlinear Schrödinger equation, Funct. Anal. and Appl., t. 10, 3, 1976, p. 209-220. | MR | Zbl

[18] N.V. Nikolenko, Invariant asymptotically stable tori of the perturbed KdV equation, Russian Math. Surveys, t. 35, 5, 1980, p. 139-207. | MR | Zbl

[19] A. Scott, F. Chu, D. Mclaughlin, The soliton: a new concept in applied science, Proc. IEEE, t. 61, 1973, p. 1443-1483. | MR

[20] V.A. Solonnikov, On general boundary value problems for elliptic systems in the sense of Douglas-Nirenberg, I, Izv. Akad. Nauk SSSR, Ser. Mat., t. 28, 1964, p. 665- 706. | MR | Zbl

[21] R. Temam, Navier-Stokes equations. Theory and numerical analysis, North-Holland, Amsterdam, 1979. | Zbl

[22] R. Temam, Navier-Stokes equations and nonlinear functional analysis, NSF/CMBS Regional Conferences Series in Applied Mathematics, SIAM, Philadelphia, 1983. | MR | Zbl

[23] G. Whitham, Linear and nonlinear waves, John Wiley, New York, 1974. | MR | Zbl

[24] V.I. Yudovich, I.I. Vorovich, Stationnary flows of incompressible viscous fluids, Math. Sborn., t. 53, 1961, p. 393-428.

[25] E. Zehnder, Siegel's linearization theorem in infinite dimension, Manuscripta Math., t. 23, 1978, p. 363-371. | MR | Zbl

[26] H. Poincaré, Thèse Paris, 1879; reprinted in Œuvres de Henri Poincaré, Vol. I, Gauthier-Villars, Paris, 1928.

[27] H. Dulac, Solutions d'un système d'équations différentielles dans le voisinage des valeurs singulières, Bull. Soc. Math. France, t. 40, 1912, p. 324-383. | JFM | Numdam | MR