메뉴 건너뛰기




Volumn 225, Issue 2, 2002, Pages 423-448

Space-time invariant measures, entropy, and dimension for stochastic Ginzburg-Landau equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036101263     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100586     Document Type: Article
Times cited : (15)

References (34)
  • 1
    • 0003796630 scopus 로고
    • [Ad] New York: Academic Press
    • [Ad] Adams, R.A.: Sobolev Spaces. New York: Academic Press, 1975
    • (1975) Sobolev Spaces
    • Adams, R.A.1
  • 3
    • 22244466122 scopus 로고    scopus 로고
    • Length scales in solutions of the complex Ginzburg-Landau equation
    • [BGO]
    • [BGO] Bartucelli, M.V., Gibbon, J.D., Oliver, M.: Length scales in solutions of the complex Ginzburg-Landau equation. Physica D 89, 267-286 (1996)
    • (1996) Physica D , vol.89 , pp. 267-286
    • Bartucelli, M.V.1    Gibbon, J.D.2    Oliver, M.3
  • 4
    • 0035539917 scopus 로고    scopus 로고
    • Ergodicity of the 2D Navier-Stokes equations with random forcing
    • [BKL]
    • [BKL] Bricmont, J., Kupiainen, A., Lefevere, R.: Ergodicity of the 2D Navier-Stokes Equations with Random Forcing. Commun. Math. Phys. 224, 65-81 (2001)
    • (2001) Commun. Math. Phys. , vol.224 , pp. 65-81
    • Bricmont, J.1    Kupiainen, A.2    Lefevere, R.3
  • 5
    • 0002723604 scopus 로고
    • Thermodynamic limit of the Ginzburg-Landau equations
    • [C1]
    • [C1] Collet, P.: Thermodynamic limit of the Ginzburg-Landau equations. Nonlinearity 7, 1175-1190 (1994)
    • (1994) Nonlinearity , vol.7 , pp. 1175-1190
    • Collet, P.1
  • 6
    • 0007380937 scopus 로고    scopus 로고
    • Extended dynamical systems
    • [C2]
    • [C2] Collet, P.: Extended Dynamical Systems, Doc. Math. Extra Volume ICM III (1998), 123-132.
    • (1998) Doc. Math. Extra Volume ICM , vol.3 , pp. 123-132
    • Collet, P.1
  • 8
    • 0033447899 scopus 로고    scopus 로고
    • Extensive properties of the complex Ginzburg-Landau equation
    • [CE1]
    • [CE1] Collet, P., Eckmann, J.-R: Extensive Properties of the Complex Ginzburg-Landau Equation, Commun. Math. Phys. 200, 699-722 (1999)
    • (1999) Commun. Math. Phys. , vol.200 , pp. 699-722
    • Collet, P.1    Eckmann, J.-R.2
  • 9
    • 0033130277 scopus 로고    scopus 로고
    • The definition and measurement of the topological entropy per unit volume in parabolic PDEs
    • [CE2]
    • [CE2] Collet, P., Eckmann, J.-R: The definition and measurement of the topological entropy per unit volume in parabolic PDEs. Nonlinearity 12, 451-473 (1999)
    • (1999) Nonlinearity , vol.12 , pp. 451-473
    • Collet, P.1    Eckmann, J.-R.2
  • 10
    • 0034356527 scopus 로고    scopus 로고
    • Topological entropy and ε-entropy for damped hyperbolic equations
    • [CE3]
    • [CE3] Collet, P., Eckmann, J.-R: Topological entropy and ε-entropy for damped hyperbolic equations. Ann. Henri Poincaré 1, 715-752 (2000)
    • (2000) Ann. Henri Poincaré , vol.1 , pp. 715-752
    • Collet, P.1    Eckmann, J.-R.2
  • 11
    • 0032325270 scopus 로고    scopus 로고
    • Hausdorff dimension of a random invariant set
    • [D]
    • [D] Debussche, A.: Hausdorff Dimension of a Random Invariant Set. J. Math. Pures Appl. 77, 967-988 (1998)
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 967-988
    • Debussche, A.1
  • 14
    • 0035218988 scopus 로고    scopus 로고
    • Invariant measures for stochastic PDE's on unbounded domains
    • [EH]
    • [EH] Eckmann, J.-P., Hairer, M.: Invariant Measures for Stochastic PDE's on Unbounded Domains. Non-linearity 14, 133-151 (2001)
    • (2001) Non-linearity , vol.14 , pp. 133-151
    • Eckmann, J.-P.1    Hairer, M.2
  • 15
    • 84972552094 scopus 로고
    • The reversible measures of multi-dimensional Ginzburg-Landau type continuum model
    • [F1]
    • [F1] Funaki, T.: The Reversible measures of Multi-Dimensional Ginzburg-Landau Type Continuum Model. Osaka J. Math. 28, 463-494 (1991)
    • (1991) Osaka J. Math. , vol.28 , pp. 463-494
    • Funaki, T.1
  • 16
    • 84972548606 scopus 로고
    • Regularity properties for stochastic partial differential equations of parabolic type
    • [F2]
    • [F2] Funaki T.: Regularity Properties for Stochastic Partial Differential Equations of Parabolic Type. Osaka J. Math. 28, 495-516 (1991)
    • (1991) Osaka J. Math. , vol.28 , pp. 495-516
    • Funaki, T.1
  • 17
    • 21844511707 scopus 로고
    • Ergodicity of the 2-D Navier-Stokes equation under random perturbations
    • [FM]
    • [FM] Flandoli, F., Maslowski, B.: Ergodicity of the 2-D Navier-Stokes equation under random perturbations. Commun. Math. Phys. 172, 119-141 (1995)
    • (1995) Commun. Math. Phys. , vol.172 , pp. 119-141
    • Flandoli, F.1    Maslowski, B.2
  • 18
    • 0001203317 scopus 로고    scopus 로고
    • The Cauchy problem in local spaces for the complex Ginzburg-Landau equation I. Compactness methods
    • [GV1]
    • [GV1] Ginibre, J., Velo G.: The Cauchy Problem in Local Spaces for the Complex Ginzburg-Landau Equation I. Compactness Methods. Physica D 95, 191-228 (1996)
    • (1996) Physica D , vol.95 , pp. 191-228
    • Ginibre, J.1    Velo, G.2
  • 19
    • 0039768823 scopus 로고    scopus 로고
    • The Cauchy problem in local spaces for the complex Ginzburg-Landau equation II. Contraction methods
    • [GV2]
    • [GV2] Ginibre, J., Velo, G.: The Cauchy Problem in Local Spaces for the Complex Ginzburg-Landau Equation II. Contraction Methods. Commun. Math. Phys. 187, 45-79 (1997)
    • (1997) Commun. Math. Phys. , vol.187 , pp. 45-79
    • Ginibre, J.1    Velo, G.2
  • 21
    • 0001646937 scopus 로고    scopus 로고
    • An analytic approach to SPDEs
    • [Kr] Carmona, R.A. and Rozovskii, B., eds., Providence, RI: Am. Math. Soc.
    • [Kr] Krylov, N.V.: An analytic approach to SPDEs. In: Stochastic partial differential equations: six perspectives. Carmona, R.A. and Rozovskii, B., eds., Providence, RI: Am. Math. Soc., 1999
    • (1999) Stochastic Partial Differential Equations: Six Perspectives
    • Krylov, N.V.1
  • 22
    • 0034349965 scopus 로고    scopus 로고
    • Stochastic dissipative PDEs and Gibbs measures
    • [KS]
    • [KS] Kuksin, S.B., Shirikyan, A.: Stochastic Dissipative PDEs and Gibbs Measures. Commun. Math. Phys. 213, 291-330 (2000)
    • (2000) Commun. Math. Phys. , vol.213 , pp. 291-330
    • Kuksin, S.B.1    Shirikyan, A.2
  • 23
    • 0003366172 scopus 로고
    • ε-entropy and ε-capacity of sets in functional spaces
    • [KT] Shiryayev, A.N., ed., Dordrecht: Kluwer
    • [KT] Kolmogorov, A.N., Tikhomirov, V.M.: ε-entropy and ε-capacity of sets in functional spaces. In: Selected Works of Kolmogorov, A.N., Vol III, Shiryayev, A.N., ed., Dordrecht: Kluwer, 1993.
    • (1993) Selected Works of Kolmogorov, A.N. , vol.3
    • Kolmogorov, A.N.1    Tikhomirov, V.M.2
  • 24
    • 0001359842 scopus 로고    scopus 로고
    • Stochastic nonlinear Schrodinger equation. 1. A priori estimates
    • [Ku]
    • [Ku] Kuksin, S.B.: Stochastic Nonlinear Schrodinger Equation. 1. A priori Estimates. Proc. Steklov Inst. Math. 225, 219-242 (1999)
    • (1999) Proc. Steklov Inst. Math. , vol.225 , pp. 219-242
    • Kuksin, S.B.1
  • 26
    • 0003263856 scopus 로고
    • Smooth ergodic theory of random dynamical systems
    • [LQ] . Berlin-Heidelberg, Springer
    • [LQ] Liu, P.-D., Qian, M.: Smooth Ergodic Theory of Random Dynamical Systems. Lecture Notes in Mathematics, 1606. Berlin-Heidelberg, Springer, 1995
    • (1995) Lecture Notes in Mathematics , vol.1606
    • Liu, P.-D.1    Qian, M.2
  • 27
    • 0033201498 scopus 로고    scopus 로고
    • Ergodicity of 2D Navier-Stokes equations with random noise and large viscosity
    • [Ma]
    • [Ma] Mattingly, J.C.: Ergodicity of 2D Navier-Stokes equations with random noise and large viscosity. Commun. Math Phys. 206, 273-288 (1999)
    • (1999) Commun. Math Phys. , vol.206 , pp. 273-288
    • Mattingly, J.C.1
  • 28
    • 0000491623 scopus 로고    scopus 로고
    • Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters
    • [Mi]
    • [Mi] Mielke, A.: Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters. Physica D 117, 106-116 (1998)
    • (1998) Physica D , vol.117 , pp. 106-116
    • Mielke, A.1
  • 30
    • 0000038026 scopus 로고
    • Large volume limit of the distribution of characteristic exponents in turbulence
    • [Ru]
    • [Ru] Ruelle, D.: Large Volume Limit of the Distribution of Characteristic Exponents in Turbulence. Commun. Math. Phys. 87, 287-302 (1982)
    • (1982) Commun. Math. Phys. , vol.87 , pp. 287-302
    • Ruelle, D.1
  • 31
    • 33751098368 scopus 로고
    • Two results concerning asymptotic behaviour of solutions of the burgers equation
    • [S]
    • [S] Sinai, Ya.G.: Two Results Concerning Asymptotic Behaviour of Solutions of the Burgers Equation. J. Statist. Phys. 64, 1-12 (1991)
    • (1991) J. Statist. Phys. , vol.64 , pp. 1-12
    • Sinai, Ya.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.