Global singularity structures of weak solutions to 4-D semilinear dispersive wave equations

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• 作者：Xu Ning and Yin Huicheng
• 关键词：Mathematics Subject Classfication (2000) 35L70 ; 35L65
• 刊名：Mathematische Zeitschrift
• 出版年：2006
• 出版时间：February 2006
• 年：2006
• 卷：252
• 期：2
• 页码：231-249
• 全文大小：225 KB

文摘

In this paper, we are concerned with the global singularity structures of weak solutions to 4-D semilinear dispersive wave equations whose initial data are chosen to be discontinuous on the unit sphere. Combining Strichartz's inequality with the commutator argument techniques, we show that the weak solutions are C2−regular away from the focusing cone surface |x|=|t−1| and the outgoing cone surface |x|=t+1.