메뉴 건너뛰기




Volumn 4, Issue 1, 1987, Pages 1-47

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

Author keywords

Asymptotic expansion; Burgers equations; Frechet space; Navier Stokes equations; Nonlinear spectral manifolds; Nonresonant spectrum; Normal forms; Parabolic nonlinear equations

Indexed keywords

ASYMPTOTIC ANALYSIS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; VISCOUS FLOW;

EID: 33747006233     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(16)30372-9     Document Type: Article
Times cited : (47)

References (28)
  • 1
    • 0003595232 scopus 로고
    • Geometrical methods in the theory of ordinary differential equations
    • Springer-Verlag New York
    • Arnold, V., Geometrical methods in the theory of ordinary differential equations. 1983, Springer-Verlag, New York.
    • (1983)
    • Arnold, V.1
  • 2
    • 84966240623 scopus 로고
    • Integrability of nonlinear differential equations via functional analysis
    • Berger, M.S., Church, P.T., Timourian, J.G., Integrability of nonlinear differential equations via functional analysis. Proc. Symp. Pure Math. t. 45:Part I (1986), 117–123.
    • (1986) Proc. Symp. Pure Math. , vol.t. 45 , pp. 117-123
    • Berger, M.S.1    Church, P.T.2    Timourian, J.G.3
  • 3
    • 1942482968 scopus 로고
    • Variétés différentiables et analytiques
    • Fascicule de résultats Hermann Paris
    • Bourbaki, N., Variétés différentiables et analytiques. Fascicule de résultats, § 1-7, 1967, Hermann, Paris.
    • (1967) , vol.§ 1-7
    • Bourbaki, N.1
  • 4
    • 0001663212 scopus 로고
    • Su un problema al contorno relativo al sistema di equazione di Stokes
    • Cattabriga, L., Su un problema al contorno relativo al sistema di equazione di Stokes. Rend. Mat. Sem. Univ. Padova t. 31 (1961), 308–340.
    • (1961) Rend. Mat. Sem. Univ. Padova , vol.t. 31 , pp. 308-340
    • Cattabriga, L.1
  • 5
    • 84990581938 scopus 로고
    • Global Lyapunov exponents, Kaplan Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations
    • Constantin, P., Foias, C., Global Lyapunov exponents, Kaplan Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations. Comm. Pure Appl. Math. t. XXXVII (1985), 1–28.
    • (1985) Comm. Pure Appl. Math. , vol.t. XXXVII , pp. 1-28
    • Constantin, P.1    Foias, C.2
  • 6
    • 85049881458 scopus 로고
    • Solutions statistiques des équations de Navier-Stokes
    • Cours au Collège de France
    • Foias, C., Solutions statistiques des équations de Navier-Stokes. 1974, Cours au Collège de France.
    • (1974)
    • Foias, C.1
  • 7
    • 0001299304 scopus 로고
    • Asymptotic behavior, as t → +∞ of solutions of Navier-Stokes equations and nonlinear spectral manifolds
    • Foias, C., Saut, J.C., Asymptotic behavior, as t → +∞ of solutions of Navier-Stokes equations and nonlinear spectral manifolds. Indiana Univ. Math. J. t. 33:3 (1984), 459–471.
    • (1984) Indiana Univ. Math. J. , vol.t. 33 , Issue.3 , pp. 459-471
    • Foias, C.1    Saut, J.C.2
  • 8
    • 0040730333 scopus 로고
    • On the smoothness of the nonlinear spectral manifolds of Navier-Stokes equations
    • Foias, C., Saut, J.C., On the smoothness of the nonlinear spectral manifolds of Navier-Stokes equations. Indiana Univ. Math. J. t. 33:6 (1984), 911–926.
    • (1984) Indiana Univ. Math. J. , vol.t. 33 , Issue.6 , pp. 911-926
    • Foias, C.1    Saut, J.C.2
  • 9
    • 0040885679 scopus 로고
    • Transformation fonctionnelle linéarisant les équations de Navier-Stokes
    • Foias, C., Saut, J.C., Transformation fonctionnelle linéarisant les équations de Navier-Stokes. C. R. Acad. Sci. Paris, Série I, Math. t. 295 (1982), 325–327.
    • (1982) C. R. Acad. Sci. Paris, Série I, Math. , vol.t. 295 , pp. 325-327
    • Foias, C.1    Saut, J.C.2
  • 10
    • 85051766280 scopus 로고    scopus 로고
    • Remarks on the spectrum of some self-adjoint operators, in preparation.
    • C. Foias, J. C. Saut, Remarks on the spectrum of some self-adjoint operators, in preparation.
    • Foias, C.1    Saut, J.C.2
  • 11
    • 84980193643 scopus 로고
    • Korteweg de Vries equations, VI: Methods for exact solution
    • Gardner, C., Greene, J., Kruskal, M., Miura, R., Korteweg de Vries equations, VI: Methods for exact solution. Comm. Pure Appl. Math. t. 27 (1974), 97–133.
    • (1974) Comm. Pure Appl. Math. , vol.t. 27 , pp. 97-133
    • Gardner, C.1    Greene, J.2    Kruskal, M.3    Miura, R.4
  • 12
    • 38249042945 scopus 로고
    • Long time behavior of solutions of abstract inequalities. Application to thermohydraulic and M. H. D. equations
    • Ghidaglia, J.M., Long time behavior of solutions of abstract inequalities. Application to thermohydraulic and M. H. D. equations. J. Diff. Eq. t. 61:2 (1986), 268–294.
    • (1986) J. Diff. Eq. , vol.t. 61 , Issue.2 , pp. 268-294
    • Ghidaglia, J.M.1
  • 13
    • 33744759548 scopus 로고
    • Remarques à propos du comportement lorsque t → ∞ des solutions des équations de Navier-Stokes associées à une force nulle
    • Guillope, C., 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), 151–180.
    • (1983) Bull. Soc. Math. France , vol.t. 111 , pp. 151-180
    • Guillope, C.1
  • 15
    • 66149163937 scopus 로고
    • Remarques sur l'unicité de la solution stationnaire d'une équation de type Navier-Stokes
    • Minea, G., Remarques sur l'unicité de la solution stationnaire d'une équation de type Navier-Stokes. Revue Roumaine Math. Pures Appl. t. 21 (1976), 1071–1075.
    • (1976) Revue Roumaine Math. Pures Appl. , vol.t. 21 , pp. 1071-1075
    • Minea, G.1
  • 16
    • 84956270766 scopus 로고
    • Complete integrability of the nonlinear Schrödinger equation
    • Nikolenko, N.V., Complete integrability of the nonlinear Schrödinger equation. Soviet Math. Dokl. t. 17:2 (1976), 398–402.
    • (1976) Soviet Math. Dokl. , vol.t. 17 , Issue.2 , pp. 398-402
    • Nikolenko, N.V.1
  • 17
    • 34250291790 scopus 로고
    • On the complete integrability of the nonlinear Schrödinger equation
    • Nikolenko, N.V., On the complete integrability of the nonlinear Schrödinger equation. Funct. Anal. and Appl. t. 10:3 (1976), 209–220.
    • (1976) Funct. Anal. and Appl. , vol.t. 10 , Issue.3 , pp. 209-220
    • Nikolenko, N.V.1
  • 18
    • 52049094701 scopus 로고
    • Invariant asymptotically stable tori of the perturbed KdV equation
    • Nikolenko, N.V., Invariant asymptotically stable tori of the perturbed KdV equation. Russian Math. Surveys t. 35:5 (1980), 139–207.
    • (1980) Russian Math. Surveys , vol.t. 35 , Issue.5 , pp. 139-207
    • Nikolenko, N.V.1
  • 19
    • 0015671259 scopus 로고
    • The soliton: a new concept in applied science
    • Scott, A., Chu, F., Mclaughlin, D., The soliton: a new concept in applied science. Proc. IEEE t. 61 (1973), 1443–1483.
    • (1973) Proc. IEEE , vol.t. 61 , pp. 1443-1483
    • Scott, A.1    Chu, F.2    Mclaughlin, D.3
  • 20
    • 0011573394 scopus 로고
    • On general boundary value problems for elliptic systems in the sense of Douglas-Nirenberg, I
    • Solonnikov, V.A., On general boundary value problems for elliptic systems in the sense of Douglas-Nirenberg, I. Izv. Akad. Nauk SSSR, Ser. Mat. t. 28 (1964), 665–706.
    • (1964) Izv. Akad. Nauk SSSR, Ser. Mat. , vol.t. 28 , pp. 665-706
    • Solonnikov, V.A.1
  • 21
    • 0003887517 scopus 로고
    • Navier-Stokes equations. Theory and numerical analysis
    • North-Holland Amsterdam
    • Temam, R., Navier-Stokes equations. Theory and numerical analysis. 1979, North-Holland, Amsterdam.
    • (1979)
    • Temam, R.1
  • 22
    • 0003872101 scopus 로고
    • Navier-Stokes equations and nonlinear functional analysis
    • NSF/CMBS Regional Conferences Series in Applied Mathematics SIAM Philadelphia
    • Temam, R., Navier-Stokes equations and nonlinear functional analysis. NSF/CMBS Regional Conferences Series in Applied Mathematics, 1983, SIAM, Philadelphia.
    • (1983)
    • Temam, R.1
  • 23
    • 0004181419 scopus 로고
    • Linear and nonlinear waves
    • John Wiley New York
    • Whitham, G., Linear and nonlinear waves. 1974, John Wiley, New York.
    • (1974)
    • Whitham, G.1
  • 24
    • 0041009480 scopus 로고
    • Stationnary flows of incompressible viscous fluids
    • Yudovich, V.I., Vorovich, I.I., Stationnary flows of incompressible viscous fluids. Math. Sborn. t. 53 (1961), 393–428.
    • (1961) Math. Sborn. , vol.t. 53 , pp. 393-428
    • Yudovich, V.I.1    Vorovich, I.I.2
  • 25
    • 0039273850 scopus 로고
    • Siegel's linearization theorem in infinite dimension
    • Zehnder, E., Siegel's linearization theorem in infinite dimension. Manuscripta Math. t. 23 (1978), 363–371.
    • (1978) Manuscripta Math. , vol.t. 23 , pp. 363-371
    • Zehnder, E.1
  • 26
    • 85051762084 scopus 로고
    • Thèse Paris; reprinted.
    • H. Poincaré Thèse Paris, 1879; reprinted.
    • (1879)
    • Poincaré, H.1
  • 27
    • 85051833226 scopus 로고
    • Œuvres de Henri Poincaré
    • Gauthier-Villars Paris
    • Œuvres de Henri Poincaré. Vol. I, 1928, Gauthier-Villars, Paris.
    • (1928) , vol.I
  • 28
    • 0000077159 scopus 로고
    • Solutions d'un système d’équations différentielles dans le voisinage des valeurs singulières
    • Dulac, H., Solutions d'un système d’équations différentielles dans le voisinage des valeurs singulières. Bull. Soc. Math. France t. 40 (1912), 324–383.
    • (1912) Bull. Soc. Math. France , vol.t. 40 , pp. 324-383
    • Dulac, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.