A new proof of scattering below the ground state for the non-radial focusing NLS

被引：43

作者：

Dodson, Benjamin ^{[1
]}

Murphy, Jason ^{[2
]}

机构：

[1] Johns Hopkins Univ, Dept Math, 404 Krieger Hall,3400 N Charles St, Baltimore, MD 21218 USA

[2] Missouri Univ Sci & Technol, Dept Math & Stat, 202 Rolla Bldg,400 W 12th St, Rolla, MO 65409 USA

来源：

MATHEMATICAL RESEARCH LETTERS | 2018年 / 25卷 / 06期

基金：

美国国家科学基金会;

关键词：

NONLINEAR SCHRODINGER-EQUATION;

D O I：

10.4310/MRL.2018.v25.n6.a5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We revisit the scattering result of Duyckaerts, Holmer, and Roudenko for the non-radial (H)over dot(1)(/2) -critical focusing NLS. By proving an interaction Morawetz inequality, we give a simple proof of scattering below the ground state in dimensions d >= 3 that avoids the use of concentration compactness.

引用

页码：1805 / 1825

页数：21

共 18 条

[1]

Cazenave T., Courant Lecture Notes in Mathematics, V10

[2] Maximal functions associated to filtrations [J].

Christ, M ;

Kiselev, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 179 (02) :409-425

[3] Global existence and scattering for rough solutions of a nonlinear Schrodinger equation on R3 [J].

Colliander, J ;

Keel, M ;

Staffilani, G ;

Takaoka, H ;

Tao, T .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (08) :987-1014

[4]

Dodson B., ARXIV14091950

[5] A NEW PROOF OF SCATTERING BELOW THE GROUND STATE FOR THE 3D RADIAL FOCUSING CUBIC NLS [J].

Dodson, Benjamin ;

Murphy, Jason .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (11) :4859-4867

[6] Global well-posedness and scattering for the mass critical nonlinear Schrodinger equation with mass below the mass of the ground state [J].

Dodson, Benjamin .

ADVANCES IN MATHEMATICS, 2015, 285 :1589-1618

[7] Scattering Norm Estimate Near the Threshold for Energy-critical Focusing Semilinear Wave Equation [J].

Duyckaerts, Thomas ;

Merle, Frank .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (04) :1971-2001

[8]

Duyckaerts T, 2008, MATH RES LETT, V15, P1233

[9] Scattering for the focusing energy-subcritical nonlinear Schrodinger equation [J].

Fang DaoYuan ;

Xie Jian ;

Cazenave Thierry .

SCIENCE CHINA-MATHEMATICS, 2011, 54 (10) :2037-2062

[10] SMOOTHING PROPERTIES AND RETARDED ESTIMATES FOR SOME DISPERSIVE EVOLUTION-EQUATIONS [J].

GINIBRE, J ;

VELO, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 144 (01) :163-188

← 1 2 →