Scattering for the focusing energy-subcritical nonlinear Schrodinger equation

被引：89

作者：

Fang DaoYuan ^{[1
]}

Xie Jian ^{[1
,2
]}

Cazenave Thierry ^{[1
,3
,4
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China

[3] Univ Paris 06, F-75252 Paris 05, France

[4] CNRS, Lab Jacques Louis Lions, F-75252 Paris 05, France

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 10期

基金：

中国国家自然科学基金; 浙江省自然科学基金;

关键词：

nonlinear Schrodinger equation; scattering; mass-supercritical and energy-subcritical; CAUCHY-PROBLEM; KLEIN-GORDON; BLOWING-UP; EXISTENCE;

D O I：

10.1007/s11425-011-4283-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the 3D focusing cubic nonlinear Schrodinger equation, scattering of H (1) solutions inside the (scale invariant) potential well was established by Holmer and Roudenko (radial case) and Duyckaerts et al. (general case) in 2008. In this paper, we extend this result to arbitrary space dimensions and focusing, mass-supercritical and energy-subcritical power nonlinearities, by adapting the method of Duyckaerts et al.

引用

页码：2037 / 2062

页数：26

共 26 条

[1]

AKAHORI T, ARXIV10061485V4

[2] High frequency approximation of solutions to critical nonlinear wave equations [J].

Bahouri, H ;

Gérard, P .

AMERICAN JOURNAL OF MATHEMATICS, 1999, 121 (01) :131-175

[3]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[4]

BERESTYCKI H, 1981, CR ACAD SCI I-MATH, V293, P489

[5] RAPIDLY DECAYING SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION [J].

CAZENAVE, T ;

WEISSLER, FB .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 147 (01) :75-100

[6]

Cazenave T, 2003, Semilinear Schrodinger Equations

[7]

Duyckaerts T, 2008, MATH RES LETT, V15, P1233

[8]

GERARD P., 1998, ESAIM Control Optim. Calc. Var., V3, P213

[9]

GIDAS, 1981, ADV MATH SUPPL STU A, V7, P369

[10]

GINIBRE J, 1985, J MATH PURE APPL, V64, P363

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