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非線性Schr塪inger方程長時穩(wěn)定性的一個估計

2023-04-29 13:47:01李海闊
關(guān)鍵詞:穩(wěn)定性方程

李海闊

References:

[1] Bambusi D. Birkhoff normal form for some nonlinear PDEs [J]. Comm Math Phys, 2003, 234: 253.

[2] Bambusi D, Delort J M, Grébert B, et al. Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds [J]. Comm Pure Appl Math, 2007, 60: 1665.

[3] Bambusi D, Grébert B. Birkhoff normal form for partial differential equations with tame modulus [J]. Duke Math J, 2006, 135: 507.

[4] Bernier J, Faou E, Grébert B. Rational normal forms and stability of small solutions to nonlinear Schrdinger equations [J]. Ann PDE, 2020, 6: 14.

[5] Bernier J, Grébert B. Long time dynamics for generalized Korteweg-de vries and Benjamin-ono equations [J]. Arch Ration Mech Anal, 2021, 241: 1139.

[6] Berti M, Delort J M. Almost global solutions of capillary-gravity water waves equations on the circle [M]. New York: Springer, 2018.

[7] Bourgain J. On diffusion in high-dimensional Hamiltonian systems and PDE [J]. J Anal Math, 2000, 80: 1.

[8] Faou E, Grébert B. A Nekhoroshev-type theorem for the nonlinear Schrdinger equation on the torus [J]. Anal PDE, 2013, 6: 1243.

[9] Grébert B, Imekraz R, Paturel . Normal forms for semilinear quantum harmonic oscillators [J]. Comm Math Phys, 2009, 291: 763.

[10] Yuan X, Zhang J. Long time stability of Hamiltonian partial differential equations [J]. SIAM J Math Anal, 2014, 46: 3176.

[11] Yuan X, Zhang J. Averaging principle for the KdV equation with a small initial value [J]. Nonlinearity, 2016, 29: 603.

[12] Bambusi D, Maiocchi A, Turri L. A large probability averaging theorem for the defocusing NLS [J]. Nonlinearity, 2019, 32: 3661.

[13] Bourgain J. Periodic nonlinear Schrdinger equation and invariant measures [J]. Comm Math Phys, 1994, 166: 1.

[14] Bourgain J. Global solutions of nonlinear Schrdinger equations [M]. Providence: AMS, 1999.

[15] Gross L. Abstract Wiener spaces [C]//Proc Fifth Berkeley Symp Math Statist and Probability. Berkeley: University of California Press, 1967.

[16] Kuo H H. Gaussian measures in Banach spaces [M]. Berlin: Springer-Verlag, 1975.

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