Global Well-Posedness for the Defocusing, Cubic, Nonlinear Wave Equation in Three Dimensions for Radial Initial Data in <(H)over dot> x <(H)over dot>s-1, s > 1/2

被引：2
|
作者：
Dodson, Benjamin [1 ]
机构：
[1] Johns Hopkins Univ, 404 Krieger Hall,3400 N Charles St, Baltimore, MD 21218 USA
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2019年 / 2019卷 / 21期
基金：
美国国家科学基金会;
关键词：
SCHRODINGER-EQUATION; LOCAL EXISTENCE; ROUGH SOLUTIONS; SCATTERING; REGULARITY;
D O I：
10.1093/imrn/rnx323
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the defocusing, cubic nonlinear wave equation in three dimensions with radial initial data. The critical space is <(H)over dot>(1/2) x <(H)over dot>(-1/2) . We show that if the initial data is radial and lies in (<(H)over dot>(s) x <(H)over dot>(s-1)) boolean AND (<(H)over dot>(1/2) x <(H)over dot>(-1/2)) for some , then the cubic initial value problem is globally well-posed. The proof utilizes the I-method, long time Strichartz estimates, and local energy decay. This method is quite similar to the method used in [11].
引用
收藏
页码：6797 / 6817
页数：21
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