Low regularity solutions of two fifth-order KDV type equations

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 Kawah...

Full description

Saved in:
Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2009, Vol.107 (1), p.221-238
Main Authors: Chen, Wengu, Li, Junfeng, Miao, Changxing, Wu, Jiahong
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-009-0009-0