Global existence for rough solutions of a fourth-order nonlinear wave equation

被引：4
|
作者：
Zhang, Junyong [1 ]
机构：
[1] China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 369卷 / 02期
关键词：
Fourth-order wave equation; Low regularity; Strichartz-type estimate; Global well-posedness; WELL-POSEDNESS; SCATTERING; REGULARITY;
D O I：
10.1016/j.jmaa.2010.04.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in H-s(R-n) for s > min{n-2/n, n/4} by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：635 / 644
页数：10
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