Bilinear space-time estimates for linearised KP-type equations on the three-dimensional torus with applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:357

Article

Gruenrock, Axel

关键词: Local and global well-posedness;    KP-II equation;   

DOI  :  10.1016/j.jmaa.2009.04.029

来源: Elsevier

【 摘 要 】

A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space-time estimates for this equation are obtained. Applications to the local and global well-posedness of dispersion generalised KP-II equations are discussed. Especially it is proved that the periodic boundary value problem for the original KP-II equation is locally well-posed for data in the anisotropic Sobolev spaces (HxHxs)-H-s(T-3), if s >= (1)/(2)and epsilon > 0. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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