SCATTERING THRESHOLD FOR THE FOCUSING NONLINEAR KLEIN-GORDON EQUATION

被引：99
作者：
Ibrahim, Slim [1 ]
Masmoudi, Nader [2 ]
Nakanishi, Kenji [3 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8P 5C3, Canada
[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[3] Kyoto Univ, Dept Math, Kyoto 6068502, Japan
来源：
ANALYSIS & PDE | 2011年 / 4卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
nonlinear Klein-Gordon equation; scattering theory; blow-up solution; ground state; Sobolev critical exponent; Trudinger-Moser inequality; GLOBAL WELL-POSEDNESS; SCHRODINGER-EQUATION; ENERGY SCATTERING; STANDING WAVES; BLOW-UP; INEQUALITY; INSTABILITY; DIMENSIONS; EXISTENCE; SPACE;
D O I：
10.2140/apde.2011.4.405
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig and Merle for the H-1 critical wave and Schrodinger equations. Our result includes the H-1 critical case, where the threshold is given by the ground state for the massless equation, and the 2D square-exponential case, where the mass for the ground state may be modified, depending on the constant in the sharp Trudinger-Moser inequality. The main difficulty is the lack of scaling invariance in both the linear and the nonlinear terms.
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页码：405 / 460
页数：56
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