A local well-posed result for the fifth order KP-II initial value problem

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• 作者：Junfeng Li^a ; ^{junfli@yahoo.com.cn} ; Shaoguang Shi^b ; ^c ; ^{shishaoguang@yahoo.com.cn}
• 关键词：Kadomtsev&ndash ; Petviashvili-II equation ; Well-posedness ; Strichartz estimates ; Bilinear estimates
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：15 June, 2013
• 年：2013
• 卷：402
• 期：2
• 页码：679-692
• 全文大小：431 K

文摘

The well-posedness of the real valued fifth order KP-II equation in Sobolev spaces has been studied by several authors. It was known to be locally well-posed in for (see Hadac (2008)?, Isaza et?al. (2006)?). We are more interested in the case . We obtain the local well-posedness for , which improves previous results by Saut and Tzvetkov (2000)? and by Isaza, L¨®pez and Mej¨ªa (2006)?. Moreover our main contribution is that we set up the global in time Strichartz estimates for the fifth order KP equation (no matter KP-I or KP-II equation) on dyadic pieces. And especially, on the low frequency part, we obtain a estimate, in which we obtain regularity which comes from the effect of term.