Low regularity solutions of two fifth-order KdV type equations
| dc.creator | Chen, Wengu | |
| dc.creator | Li, Junfeng | |
| dc.creator | Miao, Changxing | |
| dc.creator | Wu, Jiahong | |
| dc.date | 2007-10-15 | |
| dc.date | 2009-04-07 | |
| dc.date.accessioned | 2026-07-07T13:00:28Z | |
| dc.date.available | 2026-07-07T13:00:28Z | |
| dc.description | The Kawahara and modified Kawahara equations are fifth-order KdV type equations and 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 Kawahara equation in $H^s({\mathbf R})$ with $s>-\frac74$ and the local well-posedness for the modified Kawahara equation in $H^s({\mathbf R})$ with $s\ge-\frac14$. 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 \cite{Tao2001} and use this to obtain new bilinear and trilinear estimates in suitable Bourgain spaces. | |
| dc.description | 17pages | |
| dc.identifier | https://arxiv.org/abs/0710.2704 | |
| dc.identifier | http://arxiv.org/abs/0710.2704 | |
| dc.identifier | Journal D'Analyses Mathematique, Vol.107(2009)221-238 | |
| dc.identifier | doi:10.1007/s11854-009-0009-0 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225849 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q53, 35B30, 76B45 | |
| dc.title | Low regularity solutions of two fifth-order KdV type equations | |
| dc.type | text |