Low regularity solutions of two fifth-order KDV type equations

被引：6
作者：
Wengu Chen
Junfeng Li
Changxing Miao
Jiahong Wu
机构：
[1] Institute of Applied Physics and Computational Mathematics,College of Mathematics
[2] Beijing Normal University,Department of Mathematics
[3] Oklahoma State University,undefined
来源：
Journal d'Analyse Mathématique | 2009年 / 107卷
关键词：
Fundamental Estimate; Bilinear Estimate; Regularity Solution; Multiplier Norm; Nonlinear Dispersive Equation;
D O I：
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摘要：
The Kawahara and modified Kawahara equations are fifth-order KdV type equations that have been derived to model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for the Kawahara equation in Hs (R) with s ≥ − 7/4 and the local well-posedness for the modified Kawahara equation in Hs (R) with s ≥ − 1/4. To prove these results, we derive a fundamental estimate on dyadic blocks for the Kawahara equation through the [k; Z]_multiplier norm method of Tao [14] and use this to obtain new bilinear and trilinear estimates in suitable Bourgain spaces.
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