The Cauchy Problem of Null Form Wave Equation on Td with Random Initial Data

被引：1
|
作者：
Zhong, Sijia [1 ,2 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
[2] Kyoto Univ, Kyoto 6068501, Japan
来源：
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2012年 / 55卷 / 03期
关键词：
Wave equations; Null form; Random initial data; LOCAL WELL-POSEDNESS; GLOBAL EXISTENCE;
D O I：
10.1619/fesi.55.367
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the local well-posedness of the wave equation with null form nonlinearities under the periodic boundary condition. First, we prove the local existence based on some L-p-based Sobolev like Space (H) over cap (s,p), where s > 1/2 + d/p' for d >= 2, s >= 1/2, for d = 1. Second, we prove the local existence for randomized initial data in H-s with s > 1/2 and d >= 2.
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页码：367 / 403
页数：37
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