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.

引用

页码：367 / 403

页数：37

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