A Determination of the Blowup Solutions to the Focusing NLS with Mass Equal to the Mass of the Soliton

被引：4

作者：

Dodson, Benjamin ^{[1
]}

机构：

[1] Johns Hopkins Univ, Baltimore, MD 21218 USA

来源：

ANNALS OF PDE | 2023年 / 9卷 / 01期

关键词：

NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; CAUCHY-PROBLEM; POSITIVE SOLUTIONS; MINIMAL-MASS; SCATTERING; EXISTENCE; UNIQUENESS; STABILITY;

D O I：

10.1007/s40818-022-00142-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove rigidity for blowup solutions to the focusing, mass-critical nonlinear Schrodinger equation in dimensions 2 <= d <= 15 with mass equal to the mass of the soliton. We prove that the only such solutions are the solitons and the pseudoconformal transformation of the solitons. We show that this implies a Liouville result for the nonlinear Schrodinger equation.

引用

页数：86

共 41 条

[1]

Benjamin Dodson, 2016, AM J MATH, V138, P531, DOI [10.1353/ajm.2016.00161341.35149, DOI 10.1353/AJM.2016.00161341.35149]

[2] AN ODE APPROACH TO THE EXISTENCE OF POSITIVE SOLUTIONS FOR SEMI-LINEAR PROBLEMS IN RN [J].