Linearization and normal form of the Navier-Stokes equations with potential forces
Tài liệu tham khảo
Arnold, 1983
Berger, 1986, Integrability of nonlinear differential equations via functional analysis, Proc. Symp. Pure Math., t. 45, 117, 10.1090/pspum/045.1/843553
Bourbaki, 1967, § 1-7
Cattabriga, 1961, Su un problema al contorno relativo al sistema di equazione di Stokes, Rend. Mat. Sem. Univ. Padova, t. 31, 308
Constantin, 1985, Global Lyapunov exponents, Kaplan Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations, Comm. Pure Appl. Math., t. XXXVII, 1, 10.1002/cpa.3160380102
Foias, 1974
Foias, 1984, Asymptotic behavior, as t → +∞ of solutions of Navier-Stokes equations and nonlinear spectral manifolds, Indiana Univ. Math. J., t. 33, 459, 10.1512/iumj.1984.33.33025
Foias, 1984, On the smoothness of the nonlinear spectral manifolds of Navier-Stokes equations, Indiana Univ. Math. J., t. 33, 911, 10.1512/iumj.1984.33.33049
Foias, 1982, Transformation fonctionnelle linéarisant les équations de Navier-Stokes, C. R. Acad. Sci. Paris, Série I, Math., t. 295, 325
C. Foias, J. C. Saut, Remarks on the spectrum of some self-adjoint operators, in preparation.
Gardner, 1974, Korteweg de Vries equations, VI: Methods for exact solution, Comm. Pure Appl. Math., t. 27, 97, 10.1002/cpa.3160270108
Ghidaglia, 1986, Long time behavior of solutions of abstract inequalities. Application to thermohydraulic and M. H. D. equations, J. Diff. Eq., t. 61, 268, 10.1016/0022-0396(86)90121-X
Guillope, 1983, 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, 151, 10.24033/bsmf.1983
Hopf, 1950, The partial differential equation ut + uux = μuxx, Comm. Pure Appl. Math., t. 3, 201, 10.1002/cpa.3160030302
Minea, 1976, Remarques sur l’unicité de la solution stationnaire d’une équation de type Navier-Stokes, Revue Roumaine Math. Pures Appl., t. 21, 1071
Nikolenko, 1980, Invariant asymptotically stable tori of the perturbed KdV equation, Russian Math. Surveys, t. 35, 139, 10.1070/RM1980v035n05ABEH001929
Scott, 1973, The soliton: a new concept in applied science, Proc. IEEE, t. 61, 1443, 10.1109/PROC.1973.9296
Solonnikov, 1964, On general boundary value problems for elliptic systems in the sense of Douglas-Nirenberg, I, Izv. Akad. Nauk SSSR, Ser. Mat., t. 28, 665
Temam, 1979
Temam, 1983
Yudovich, 1961, Stationnary flows of incompressible viscous fluids, Math. Sborn., t. 53, 393
H. Poincaré, Thèse Paris, 1879; reprinted.
1928, Vol. I
Dulac, 1912, Solutions d’un système d’équations différentielles dans le voisinage des valeurs singulières, Bull. Soc. Math. France, t. 40, 324, 10.24033/bsmf.910
Whitham, 1974