Well-posedness for the fifth order KP-II initial data problem in

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• 作者：Junfeng Li^a ; ^{lijunfeng@bnu.edu.cn} ; Xia Li^b ; ^{lixia861015@mail.bnu.edu.cn}
• 关键词：35Q53 ; 37K10
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2196-2230
• 全文大小：421 K
• 卷排序：262

文摘

The well-posed properties for the fifth order KP-II initial value problem for x∈Rx∈R, y∈Ty∈T are considered. It is proved to be locally well posed in Hs,0(R×T)Hs,0(R×T) for s≥−34 with small initial data and s>−34 with general initial data. By the L2L2 conservation law of KP equation, the L2L2 global well-posedness is also obtained. The crucial ingredient of the argument is the L2L2 estimates of a bilinear operator which was introduced in recent works [14] and [13]. This operator is Galilean invariant in the content of T2T2 and R2R2 but not in the content R×TR×T.