Scattering theory for nonlinear Schrodinger equations with inverse-square potential

被引：57

作者：

Zhang, Junyong ^{[1
,2
,3
]}

Zheng, Jiqiang ^{[4
,5
]}

机构：

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[3] Australian Natl Univ, Dept Math, Canberra, ACT 0200, Australia

[4] Univ Nice Sophia Antipolis, F-06108 Nice 02, France

[5] Inst Univ France, Paris, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 267卷 / 08期

基金：

中国国家自然科学基金; 澳大利亚研究理事会; 北京市自然科学基金;

关键词：

Nonlinear Schrodinger equation; Inverse square potential; Interaction Morawetz estimates; Scattering; CAUCHY-PROBLEM; WAVE-EQUATION; CONICAL ENDS; DECAY; EVOLUTIONS; MANIFOLDS; OPERATORS; ROUGH;

D O I：

10.1016/j.jfa.2014.08.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the long-time behavior of solutions to nonlinear Schrodinger equations with some critical rough potential of a vertical bar x vertical bar(-2) type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with P-a = -Delta + a vertical bar x vertical bar(-2). We use such properties to obtain the scattering theory for the defocusing energy-subcritical nonlinear Schrodinger equation with inverse square potential in energy space H-1(R-n). (C) 2014 Published by Elsevier Inc.

引用

页码：2907 / 2932

页数：26

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