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

Sun Chenmin; Wang Hua; Yao Xiaohua; Zheng Jiqiang

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

机译：径向数据聚焦分数阶非线性Schedederer方程在地表下的散射

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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.

机译：本文的目的是调整H中的策略[参见B. Dodson，J. Murphy，3D径向聚焦立方NLS的基态以下散射的新证明，arXiv：1611.04195]以证明径向散射某些聚焦分数NLS低于锐利阈值的解。主要成分是应用[3]中证明的分数病毒身份[参见，T。Boulenger，D。Himmelsbach，E。Lenzmann，炸毁分数NLS，J。功能Anal，271（2016），2569-2603]以排除原点附近的质量集中。

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来源
《Discrete and continuous dynamical systems》 |2018年第4期|2207-2228|共22页
作者
Sun Chenmin; Wang Hua; Yao Xiaohua; Zheng Jiqiang;
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作者单位

Univ Cote dAzur LJAD F-06100 Nice France;

Cent China Normal Univ Dept Math Wuhan 430079 Hubei Peoples R China|Cent China Normal Univ Hubei Prov Key Lab Math Phys Wuhan 430079 Hubei Peoples R China;

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正文语种 eng
中图分类
关键词
Fractional Schrodinger equation; scattering; Morawetz estimate;

机译：分数薛定inger方程;散射;Morawetz估计;

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1. THE SOBOLEV-MORAWETZ APPROACH FOR THE ENERGY SCATTERING OF NONLINEAR SCHROEDINGER-TYPE EQUATIONS WITH RADIAL DATA [J] . VAN DUONG DINH, SAHBI KERAANI Discrete and Continuous Dynamical Systems,Series S . 2021,第8期

机译：具有径向数据的非线性Schroedinger型方程能量散射的SoboLev-Morawetz方法
2. GROUND STATES OF NONLINEAR SCHROEDINGER EQUATIONS WITH FRACTIONAL LAPLACIANS [J] . ZUPEI SHEN, ZHIQING HAN, QINQIN ZHANG Discrete and continuous dynamical systems▼hSeries S . 2019,第7期

机译：具有分数拉普拉斯的非线性施德林格方程的地面态
3. GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE DEFOCUSING, CUBIC NONLINEAR SCHROEDINGER EQUATION WHEN n = 3 VIA A LINEAR-NONLINEAR DECOMPOSITION [J] . Benjamin Dodson Discrete and continuous dynamical systems . 2013,第5期

机译：当n = 3通过线性-非线性分解时，去立方立方非线性Schroedinger方程的全局适定性和散射
4. FRACTIONAL GENERALIZATION OF GINZBURG-LANDAU AND NONLINEAR SCHROEDINGER EQUATIONS [C] . George M. Zaslavsky, Vasily E. Tarasov American Society of Mechanical Engineers(ASME)International Design Engineering Technical Conference and Computers and Information in Engineering Conference(DETC2005) vol.6 pt.6: International Conference on Multibody Systems, Nonlinear Dynamics, and Contr . 2005

机译：GINZBURG-LANDAU的分数阶广义和非线性Schroedinger方程
5. The defocusing energy-critical nonlinear Schroedinger equation in dimensions five and higher. [D] . Visan, Monica. 2006

机译：散焦能量临界非线性Schroedinger方程，尺寸为5或更高。
6. On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation [O] . Chris W. Wahle, David S. Ross, George M. Thurston -1

机译：基于非线性偏微分方程的静态光散射数据确定三元混合自由能的实验设计
7. Inverse scattering transform for the discrete focusing nonlinear schroedinger equation with nonvanishing boundary conditions [O] . Van der Mee C 2015

机译：边界条件不变的离散聚焦非线性薛定inger方程的逆散射变换

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

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