Scattering and Blow-Up Dichotomy of the Energy-Critical Nonlinear Schrödinger Equation With the Inverse-Square Potential

被引：0

作者：

Hamano, Masaru ^{[1
]}

Ikeda, Masahiro ^{[2
,3
]}

机构：

[1] Waseda Univ, Fac Sci & Engn, Tokyo, Japan

[2] RIKEN Ctr Adv Intelligence Project, Tokyo, Japan

[3] Keio Univ, Fac Sci & Technol, Dept Math, Yokohama, Japan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年 / 48卷 / 08期

关键词：

inverse-square potential; nonlinear Schr & ouml; dinger equation; scattering; blow-up; GLOBAL WELL-POSEDNESS; SCHRODINGER-EQUATION; THRESHOLD SOLUTIONS; GROUND-STATE; CRITICAL NLS; PROOF; H-1;

D O I：

10.1002/mma.10794

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the energy critical nonlinear Schr & ouml;dinger equation with a repulsive inverse square potential. In particular, we deal with radial initial data, whose energy is equal to the energy of static solution to the corresponding nonlinear Schr & ouml;dinger equation without a potential. We investigate time behavior of the radial solutions with such initial data.

引用

页码：9225 / 9240

页数：16

共 47 条

[1] Blowup and scattering problems for the nonlinear Schrodinger equations [J].