Low regularity solutions of two fifth-order KDV type equations |
| |
Authors: | Wengu Chen Junfeng Li Changxing Miao Jiahong Wu |
| |
Institution: | (1) Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing, 100088, China;(2) College of Mathematics, Beijing Normal University, Beijing, 100875, China;(3) Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA |
| |
Abstract: | 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 H
s
(R) with s ≥ − 7/4 and the local well-posedness for the modified Kawahara equation in H
s
(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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|