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Volumn 5, Issue 3, 2005, Pages 317-356

Ergodicity for a weakly damped stochastic non-linear Schrödinger equation

Author keywords

Coupling method; Ergodicity; Expectational Foias Prodi estimate; Girsanov's formula; Invariant measure; Markov transition semi group; Non linear Schr dinger equations

Indexed keywords


EID: 26844527772     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-005-0195-x     Document Type: Article
Times cited : (55)

References (28)
  • 2
    • 0034348208 scopus 로고    scopus 로고
    • Inviscid limits of the Complex Ginzburg-Landau Equation
    • BEBOUCHE, P. and JÜNGEL, A., Inviscid limits of the Complex Ginzburg-Landau Equation, Commun. Math. Phys. 214 (2000), 201-226.
    • (2000) Commun. Math. Phys. , vol.214 , pp. 201-226
    • Bebouche, P.1    Jüngel, A.2
  • 3
    • 0036025910 scopus 로고    scopus 로고
    • Exponential mixing for the 2D stochastic Navier-Stokes dynamics
    • BRICMONT, A., KUPIAINEN, A. and LEFEVERE, R., Exponential mixing for the 2D stochastic Navier-Stokes dynamics, Commun. Math. Phys. 230 (2002), no. 1, 87-132.
    • (2002) Commun. Math. Phys. , vol.230 , Issue.1 , pp. 87-132
    • Bricmont, A.1    Kupiainen, A.2    Lefevere, R.3
  • 6
    • 0033175771 scopus 로고    scopus 로고
    • A stochastic non-linear Schrödinger equation with multiplicative noise
    • DE BOUARD, A. and DEBUSSCHE, A., A stochastic non-linear Schrödinger equation with multiplicative noise. Commun. Math. Phys. 205 (1999), 161-181.
    • (1999) Commun. Math. Phys. , vol.205 , pp. 161-181
    • De Bouard, A.1    Debussche, A.2
  • 8
    • 0035639506 scopus 로고    scopus 로고
    • Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation
    • MATTINGLY, W. E, J. C. and SINAI, Y. G., Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Commun. Math. Phys. 224 (2001), 83-106.
    • (2001) Commun. Math. Phys. , vol.224 , pp. 83-106
    • Mattingly, W.E.J.C.1    Sinai, Y.G.2
  • 11
    • 21844511707 scopus 로고
    • Ergodicity of the 2-D Navier-Stokes equation under random perturbations
    • FLANDOLI, F. and MASLOWSKI, B., Ergodicity of the 2-D Navier-Stokes equation under random perturbations. Commun. Math. Phys. 171 (1995), 119-141.
    • (1995) Commun. Math. Phys. , vol.171 , pp. 119-141
    • Flandoli, F.1    Maslowski, B.2
  • 12
    • 0000098780 scopus 로고
    • On the theorie of superconductivity
    • GINZBURG, V. and LANDAU, L., On the theorie of superconductivity, Zh. Eksp. Fiz. 20, 1064 (1950)
    • (1950) Zh. Eksp. Fiz. , vol.20 , pp. 1064
    • Ginzburg, V.1    Landau, L.2
  • 13
    • 0002585056 scopus 로고
    • New York: Pergammon Press
    • English transl. In: Men of Physics: L.D. Landau. Vol. I. Ter Haar (ed.). New York: Pergammon Press. (1965), 546-568.
    • (1965) Men of Physics: L.D. Landau , vol.1 , pp. 546-568
    • Haar, T.1
  • 14
    • 85064027304 scopus 로고    scopus 로고
    • Regularity of the attractor for a weakly damped nonlinear Schrödinger equation
    • GOUBET, O., Regularity of the attractor for a weakly damped nonlinear Schrödinger equation. Appl. Anal. 60 (1996), no. 1-2, 99-119.
    • (1996) Appl. Anal. , vol.60 , Issue.1-2 , pp. 99-119
    • Goubet, O.1
  • 15
    • 0036026967 scopus 로고    scopus 로고
    • Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling, Proba
    • HAIRER, M., Exponential Mixing Properties of Stochastic PDEs Through Asymptotic Coupling, Proba. Theory Related Fields, 124(3), (2002) 345-380.
    • (2002) Theory Related Fields , vol.124 , Issue.3 , pp. 345-380
    • Hairer, M.1
  • 17
    • 0001453581 scopus 로고
    • Universal Decay of vortex density in two dimensions
    • HUBER, G. and ALSTROM, P., Universal Decay of vortex density in two dimensions, Physica A 195 (1993), 448-456.
    • (1993) Physica A , vol.195 , pp. 448-456
    • Huber, G.1    Alstrom, P.2
  • 18
    • 10244265831 scopus 로고    scopus 로고
    • On exponential convergence to a stationary mesure for nonlinear PDEs
    • The M. I. Viishik Moscow PDE seminar, Amer. Math. Soc.
    • KUKSIN, S., On exponential convergence to a stationary mesure for nonlinear PDEs. The M. I. Viishik Moscow PDE seminar, Amer. Math. Soc. Trans. (2), vol 206, Amer. Math. Soc., 2002.
    • (2002) Amer. Math. Soc. Trans. (2) , vol.206
    • Kuksin, S.1
  • 19
    • 0034349965 scopus 로고    scopus 로고
    • Stochastic dissipative PDE's and Gibbs measures
    • KUKSIN, S. and SHIRIKYAN, A., Stochastic dissipative PDE's and Gibbs measures, Commun. Math. Phys. 213 (2000), 291-330.
    • (2000) Commun. Math. Phys. , vol.213 , pp. 291-330
    • Kuksin, S.1    Shirikyan, A.2
  • 20
    • 0035536788 scopus 로고    scopus 로고
    • A coupling approach to randomly forced randomly forced PDE's I
    • KUKSIN, S. and SHIRIKYAN, A., A coupling approach to randomly forced randomly forced PDE's I. Commun. Math. Phys. 227 (2001), 351-366.
    • (2001) Commun. Math. Phys. , vol.227 , pp. 351-366
    • Kuksin, S.1    Shirikyan, A.2
  • 21
    • 0036770515 scopus 로고    scopus 로고
    • A coupling approach to randomly forced randomly forced PDE's II
    • KUKSIN, S. PIATNITSKI, A. and SHIRIKYAN, A., A coupling approach to randomly forced randomly forced PDE's II. Commun. Math. Phys. 230 (2002), no. 1, 81-85.
    • (2002) Commun. Math. Phys. , vol.230 , Issue.1 , pp. 81-85
    • Kuksin, S.1    Piatnitski, A.2    Shirikyan, A.3
  • 22
    • 0036095320 scopus 로고    scopus 로고
    • Coupling approach to white-forced nonlinear PDEs
    • KUKSIN, S. and SHIRIKYAN, A., Coupling approach to white-forced nonlinear PDEs, J. Math. Pures Appl. 1 (2002), 567-602.
    • (2002) J. Math. Pures Appl. , vol.1 , pp. 567-602
    • Kuksin, S.1    Shirikyan, A.2
  • 23
    • 1842683021 scopus 로고    scopus 로고
    • Randomly forced CGL equation: Stationary measure and the inviscid limit
    • KUKSIN, S. and SHIRIKYAN, A., Randomly forced CGL equation: Stationary measure and the inviscid limit, J. Phys. A 37 (2004), no. 12, 3805-2822.
    • (2004) J. Phys. A , vol.37 , Issue.12 , pp. 3805-2822
    • Kuksin, S.1    Shirikyan, A.2
  • 24
    • 0036026973 scopus 로고    scopus 로고
    • Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics
    • Mattingly, J., Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics, Commun. Math. Phys. 230 (2002), 421-462.
    • (2002) Commun. Math. Phys. , vol.230 , pp. 421-462
    • Mattingly, J.1
  • 25
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • NEWEL, A. and WHITEHEAD, J., Finite bandwidth, finite amplitude convection, J. Fluid Mech. 38 (1969), 279-303.
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newel, A.1    Whitehead, J.2
  • 28
    • 4544351685 scopus 로고    scopus 로고
    • Exponential mixing for 2D Navier-Stokes equation pertubed by an unbounded noise
    • SHIRIKYAN, A., Exponential mixing for 2D Navier-Stokes equation pertubed by an unbounded noise, J. Math. Fluid Mech. 6 (2004), 169-193.
    • (2004) J. Math. Fluid Mech. , vol.6 , pp. 169-193
    • Shirikyan, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.