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.
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页码：1827 / 1875
页数：49
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