Well-posedness for the fifth order KP-II initial data problem in Hs,0 (R x T)

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Li, Junfeng¹  Li, Xia² 

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

[2] North Univ China, Sch Sci, Taiyuan 030051, Shanxi, Peoples R China

关键词: KP-II equation;    Initial value problem;    X-s,X-1/2,X-1;    Bilinear estimates;   

DOI  :  10.1016/j.jde.2016.10.048

来源: Elsevier

【 摘 要 】

The well-posed properties for the fifth order initial value problem for x is an element of R, y is an element of T are considered. It is proved to be locally well posed in H-s,H-0 (R x T) for s >= -3/4 with small initial data and s > -3/4 with general initial data. By the L-2 conservation law of KIP equation, the L-2 global well-posedness is also obtained. The crucial ingredient of the argument is the L-2 estimates of a bilinear operator which was introduced in recent works [14] and [13]. This operator is Galilean invariant in the content of T-2 and R-2 but not in the content R x T. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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