A Para-Differential Renormalization Technique for Nonlinear Dispersive Equations

被引：45

作者：

Herr, Sebastian ^{[1
]}

Ionescu, Alexandru D. ^{[2
]}

Kenig, Carlos E. ^{[3
]}

Koch, Herbert ^{[1
]}

机构：

[1] Univ Bonn, Math Inst, D-53115 Bonn, Germany

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[3] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2010年 / 35卷 / 10期

基金：

美国国家科学基金会;

关键词：

Dispersion generalized Benjamin-Ono equation; Frequency-dependent renormalization; Global well-posedness; L-2 initial data; GLOBAL WELL-POSEDNESS; BENJAMIN-ONO-EQUATION; KDV;

D O I：

10.1080/03605302.2010.487232

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For alpha. epsilon (1, 2) we prove that the initial-value problem Sigma partial derivative(t)u + D-alpha partial derivative(x)u + partial derivative(x) (u(2)/2) = 0 on R-x x R-t; u(0) = phi, is globally well-posed in the space of real-valued L-2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.

引用

页码：1827 / 1875

页数：49

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