SCATTERING OF THE FOCUSING ENERGY-CRITICAL NLS WITH INVERSE SQUARE POTENTIAL IN THE RADIAL CASE

被引：8

作者：

Yang, Kai ^{[1
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 211189, Jiangsu, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 01期

关键词：

Scattering; inverse square potential; ground state solution; energy critical; NLS; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; WAVE-EQUATION; BLOW-UP; EXTERIOR;

D O I：

10.3934/cpaa.2020258

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem of the focusing energy-critical nonlinear Schrodinger equation with an inverse square potential. We prove that if any radial solution obeys the supreme of the kinetic energy over the maximal lifespan is below the kinetic energy of the ground state solution, then the solution exists globally in time and scatters in both time directions.

引用

页码：77 / 99

页数：23

共 50 条

[41] Scattering in H1 for the intercritical NLS with an inverse-square potential [J].

Lu, Jing ;

Miao, Changxing ;

Murphy, Jason .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (05) :3174-3211

[42] PROFILES FOR THE RADIAL FOCUSING ENERGY-CRITICAL WAVE EQUATION IN ODD DIMENSIONS [J].

Rodriguez, Casey .

ADVANCES IN DIFFERENTIAL EQUATIONS, 2016, 21 (5-6) :505-570

[43] Global regularity for the energy-critical NLS on S3 [J].

Pausader, Benoit ;

Tzvetkov, Nikolay ;

Wang, Xuecheng .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (02) :315-338

[44] GLOBAL WELL-POSEDNESS AND SCATTERING FOR DEFOCUSING ENERGY-CRITICAL NLS IN THE EXTERIOR OF BALLS WITH RADIAL DATA [J].

Li, Dong ;

Smith, Hart ;

Zhang, Xiaoyi .

MATHEMATICAL RESEARCH LETTERS, 2012, 19 (01) :213-232

[45] The Cauchy problem of a focusing energy-critical nonlinear Schrodinger equation [J].

Huang, Juan ;

Zhang, Jian .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 80 :122-134

[46] On long time behavior of the focusing energy-critical NLS on RdxTvia semivirial-vanishing geometry [J].

Luo, Yongming .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2023, 177 :415-454

[47] Energy-critical Hartree equation with harmonic potential for radial data [J].

Wu, Haigen ;

Zhang, Junyong .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2821-2840

[48] Scattering for the Radial Focusing Inhomogeneous NLS Equation in Higher Dimensions [J].

Farah, Luiz Gustavo ;

Guzman, Carlos M. .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2020, 51 (02) :449-512

[49] THE FOCUSING ENERGY-CRITICAL FOURTH-ORDER SCHRODINGER EQUATION WITH RADIAL DATA [J].

Pausader, Benoit .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (04) :1275-1292

[50] On stability and instability of the ground states for the focusing inhomogeneous NLS with inverse-square potential [J].

An, JinMyong ;

Mun, HakBom ;

Kim, JinMyong .

PURE AND APPLIED MATHEMATICS QUARTERLY, 2024, 20 (06) :2647-2666

← 1 2 3 4 5 →