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

页码：6797 / 6817

页数：21