Scattering for the two-dimensional NLS with exponential nonlinearity

被引：19

作者：

Ibrahim, S. ^{[1
]}

Majdoub, M. ^{[2
]}

Masmoudi, N. ^{[3
]}

Nakanishi, K. ^{[4
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8P 5C3, Canada

[2] Univ Tunis El Manar, Dept Math, Fac Sci Tunis, Tunis, Tunisia

[3] NYU, Courant Inst, New York, NY 10012 USA

[4] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

来源：

NONLINEARITY | 2012年 / 25卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

SCHRODINGER-EQUATION; KLEIN-GORDON; ENERGY SPACE; INEQUALITY; POSEDNESS;

D O I：

10.1088/0951-7715/25/6/1843

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate existence and asymptotic completeness of the wave operators for nonlinear Schrodinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of the conserved Hamiltonian, below which the exponential potential energy is dominated by the kinetic energy via a Trudinger-Moser type inequality. We prove that if the Hamiltonian is below the critical value, then the solution approaches a free Schrodinger solution at the time infinity.

引用

页码：1843 / 1849

页数：7

共 21 条

[1] Trudinger type inequalities in RN and their best exponents [J].