Global well-posedness and scattering for nonlinear Schrodinger equations with combined nonlinearities in the radial case

被引：35

作者：

Cheng, Xing ^{[1
]}

Miao, Changxing ^{[2
]}

Zhao, Lifeng ^{[3
,4
]}

机构：

[1] Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

[2] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China

[3] Univ Sci & Technol China, Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China

[4] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 06期

关键词：

Nonlinear Schrodinger equation; Combined nonlinearities; Global wellposedness; Scattering; Blowup; BLOW-UP; CAUCHY-PROBLEM; GROUND-STATE; DIMENSIONS; COMPACTNESS; EXISTENCE;

D O I：

10.1016/j.jde.2016.04.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy problem for the nonlinear Schrodinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in H-1 (R-d) and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in H-1 (R-d) below the threshold for radial data when d <= 4. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：2881 / 2934

页数：54

共 50 条

[41] GLOBAL WELL-POSEDNESS FOR NONLINEAR SCHRODINGER EQUATIONS WITH ENERGY-CRITICAL DAMPING
Feng, Binhua
Zhao, Dun
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[42] Global well-posedness of the Cauchy problem for nonlinear Schrodinger-type equations
Miao, Changxing
Zhang, Bo
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2007, 17 (01) : 181 - 200
[43] GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE DEFOCUSING, L2-CRITICAL NONLINEAR SCHRODINGER EQUATION WHEN d ≥ 3
Dodson, Benjamin
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 25 (02) : 429 - 463
[44] Global well-posedness for 2D nonlinear wave equations without compact support
Cai, Yuan
Lei, Zhen
Masmoudi, Nader
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2018, 114 : 211 - 234
[45] WELL-POSEDNESS AND SCATTERING FOR FOURTH ORDER NONLINEAR SCHRODINGER TYPE EQUATIONS AT THE SCALING CRITICAL REGULARITY
Hirayama, Hiroyuki
Okamoto, Mamoru
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (03) : 831 - 851
[46] Global well-posedness for the derivative nonlinear Schrodinger equation
Bahouri, Hajer
Perelman, Galina
INVENTIONES MATHEMATICAE, 2022, 229 (02) : 639 - 688
[47] GLOBAL WELL-POSEDNESS ON THE DERIVATIVE NONLINEAR SCHRODINGER EQUATION
Wu, Yifei
ANALYSIS & PDE, 2015, 8 (05): : 1101 - 1112
[48] Global Well-Posedness for the Fractional Nonlinear Schrodinger Equation
Guo, Boling
Huo, Zhaohui
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (02) : 247 - 255
[49] Global Well-Posedness and Analytic Smoothing Effect for the Dissipative Nonlinear Schrodinger Equations
Hoshino, Gaku
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (04) : 2339 - 2351
[50] Global well-posedness and scattering of the defocusing energy-critical inhomogeneous nonlinear Schrodinger equation with radial data
Park, Dongjin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 536 (02)

← 1 2 3 4 5 →