ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

被引：47

作者：

Colliander, J. ^{[1
]}

Ibrahim, S. ^{[2
]}

Majdoub, M. ^{[3
]}

Masmoudi, N. ^{[4
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[2] Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA

[3] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

[4] NYU, Courant Inst Math Sci, Dept Math, New York, NY 10012 USA

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2009年 / 6卷 / 03期

关键词：

Nonlinear Schrodinger equation; energy critical; well-posedness; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELLPOSEDNESS; ROUGH SOLUTIONS; WELL-POSEDNESS; CAUCHY-PROBLEM; ILL-POSEDNESS; KLEIN-GORDON; SCATTERING; INEQUALITY; INSTABILITY;

D O I：

10.1142/S0219891609001927

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the initial value problem for a defocusing nonlinear Schrodinger equation with exponential nonlinearity i partial derivative(t)u + Delta u = u(e(4 pi|u|2) - 1) in R-t x R-x(2). We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

引用

页码：549 / 575

页数：27

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