SCATTERING BELOW GROUND STATE OF FOCUSING FRACTIONAL NONLINEAR SCHRODINGER EQUATION WITH RADIAL DATA

被引：12

作者：

Sun, Chenmin ^{[1
]}

Wang, Hua ^{[2
,3
]}

Yao, Xiaohua ^{[2
,3
]}

Zheng, Jiqiang ^{[1
]}

机构：

[1] Univ Cote dAzur, LJAD, F-06100 Nice, France

[2] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China

[3] Cent China Normal Univ, Hubei Prov Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 04期

基金：

美国国家科学基金会;

关键词：

Fractional Schrodinger equation; scattering; Morawetz estimate; WELL-POSEDNESS; BLOW-UP;

D O I：

10.3934/dcds.2018091

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to adapt the strategy in H [ See, B. Dodson, J. Murphy, a new proof of scattering below the ground state for the 3D radial focusing cubic NLS, arXiv:1611.04195 ] to prove the scattering of radial solutions below sharp threshold for certain focusing fractional NLS. The main ingredient is to apply the fractional virial identity proved in [3] [ See, T. Boulenger, D. Himmelsbach, E. Lenzmann, Blow up for fractional NLS,J. Func. Anal, 271(2016), 2569-2603 ] to exclude the concentration of mass near the origin.

引用

页码：2207 / 2228

页数：22

共 20 条

[1]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1

[2]

Balakrishnan A. V., 1960, Pac. J. Math, V10, P419, DOI [10.2140/pjm.1960.10.419, DOI 10.2140/PJM.1960.10.419]

[3] Blowup for fractional NLS [J].