SCATTERING BELOW THE GROUND STATE FOR THE 2d RADIAL NONLINEAR SCHRODINGER EQUATION

被引：18

作者：

Arora, Anudeep Kumar ^{[1
]}

Dodson, Benjamin ^{[2
]}

Murphy, Jason ^{[3
]}

机构：

[1] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[3] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 04期

关键词：

PROOF;

D O I：

10.1090/proc/14824

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We revisit the problem of scattering below the ground state threshold for the mass-supercritical focusing nonlinear Schrodinger equation in two space dimensions. We present a simple new proof that treats the case of radial initial data. The key ingredient is a localized virial/Morawetz estimate; the radial assumption aids in controlling the error terms resulting from the spatial localization.

引用

页码：1653 / 1663

页数：11

共 16 条

[1] Blowup and scattering problems for the nonlinear Schrodinger equations [J].

Akahori, Takafumi ;

Nawa, Hayato .

KYOTO JOURNAL OF MATHEMATICS, 2013, 53 (03) :629-672

[2]

Cazenave T., 2003, Courant Lecture Notes in Mathematics, V10, DOI DOI 10.1090/CLN/010

[3] A new proof of scattering below the ground state for the non-radial focusing NLS [J].

Dodson, Benjamin ;

Murphy, Jason .

MATHEMATICAL RESEARCH LETTERS, 2018, 25 (06) :1805-1825

[4] 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

[5]

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

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

Fang DaoYuan ;

Xie Jian ;

Cazenave Thierry .

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

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

GINIBRE, J ;

VELO, G .

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

[8] Global Behavior of Finite Energy Solutions to the d-Dimensional Focusing Nonlinear Schrodinger Equation [J].

Guevara, Cristi Darley .

APPLIED MATHEMATICS RESEARCH EXPRESS, 2014, (02) :177-243

[9]

Guo Z., ARXIV190601804

[10] A sharp condition for scattering of the radial 3D cubic nonlinear Schrodinger equation [J].

Holmer, Justin ;

Roudenko, Svetlana .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 282 (02) :435-467

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