INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

doi:10.1016/S0252-9602(11)60203-8

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 15-21.doi: 10.1016/S0252-9602(11)60203-8

INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

徐桂香|苑佳

Institute of Applied Physics and Computational Mathematics, P. O. Box 8009,\ Beijing 100088, China；School of Mathematics and Systems Science, Beihang University, LIMB of the Ministry of Education,\\ Beijing |100191, China

收稿日期:2007-05-31 修回日期:2007-08-19 出版日期:2011-01-20 发布日期:2011-01-20
基金资助:
Xu G and Yuan J were partly supported by the NSF of China (10801015, 10901012). The authors would like to thank the referee for his valuable comments and suggestions.

INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

XU Gui-Xiang, YU Jia

Institute of Applied Physics and Computational Mathematics, P. O. Box 8009,\ Beijing 100088, China；School of Mathematics and Systems Science, Beihang University, LIMB of the Ministry of Education,\\ Beijing |100191, China

Received:2007-05-31 Revised:2007-08-19 Online:2011-01-20 Published:2011-01-20
Supported by:
Xu G and Yuan J were partly supported by the NSF of China (10801015, 10901012). The authors would like to thank the referee for his valuable comments and suggestions.

摘要/Abstract

摘要：

In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz
estimate that was originally introduced in [5].

关键词: Scattering theory, Hartree equation, wave operators, asymptotic completeness

Abstract:

In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz
estimate that was originally introduced in [5].

Key words: Scattering theory, Hartree equation, wave operators, asymptotic completeness

中图分类号:

35P25

徐桂香, 苑佳. INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS[J]. 数学物理学报(英文版), 2011, 31(1): 15-21.

XU Gui-Xiang, YU Jia. INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS[J]. Acta mathematica scientia,Series B, 2011, 31(1): 15-21.

参考文献

[1] Bourgain J. Global well-posedness of defocusing 3D critical NLS in the radial case. J Amer Math Soc, 1999, 12: 145--171

[2] Bourgain J. Global solutions of nonlinear Schrödinger equations//Amer Math Soc Colloq Publ, 46. Providence: Amer Math Soc, 1999

[3] Cazenave T. An introduction to nonlinear Schrödinger equations//Textos de Métodos Matemáticos 26. Instituto de Matemática Rio de Janeiro, 1996

[4] Cazenave T, Weissler F. The Cauchy problem for the critical nonlinear Schr\"{o}dinger equation in H^s. Nonlinear
Anal T M A, 1990, 14: 807--836

[5] Colliander J, Keel M, Staffilani G, et al. Global existend and scattering for rough solutions of a nonlinear schrödinger equation on R³. Comm Pure Appl Math, 2004, 57: 987--1014

[6] Colliander J, Keel M, Staffilani G, et al. Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R³. Annals of Math, 2008, 167: 767--865

[7] Ginibre J, Velo G. On a class of nonlinear Schrödinger equations with nonlocal interaction. Math Z,1980, 170: 109--136

[8] Ginibre J, Velo G. Scattering theory in the energy space for a class of nonlinear Schr\"{o}dinger equations. J Math Pure Appl, 1985, 64: 363--401

[9] Ginibre J, Velo G. Scattering theory in the energy space for a class of Hartree equations, Nonlinear wave
equations (Providence, RI, 1998), 29--60//Contemp Math, 263. Providence, RI: Amer Math Soc, 2000

[10] Hayashi N, Ozawa T. Scattering theory in the weighted L²(Rⁿ) spaces for some Schrödinger equations. Ann Inst H Poincaré Phys Théor, 1988, 48: 17--37

[11] Hayashi N, Tsutsumi Y. Scattering theory for Hartree type equations. Ann Inst H Poincaré Phys Théor, 1987, 46: 187--213

[12] Nakanishi K. Energy scattering for nonlinear Klein-Gordon and Schröinger equations in spatial dimensions 1 and 2. J Funct Anal, 1999, 169(1): 201--225

[13] Nakanishi K. Energy scattering for Hartree equations. Math Res Lett, 1999, 6: 107--118

[14] Nakanishi K. Remarks on the energy scattering for nonlinear Klein-Gordon and Schröinger equations. Tohoku Math J, II, 2001, 53(2): 285--303

[15] Nawa H, Ozawa T. Nonlinear scattering with nonlocal interaction. Comm Math Phys, 1992, 146: 259--275

INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

INTERACTION MORAWETZ ESTIMATE AND A SIMPLIFIED PROOF ON THE ENERGY SCATTERING FOR HARTREE EQUAITONS

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