Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$
| dc.creator | Colliander, J. | |
| dc.creator | Keel, M. | |
| dc.creator | Staffilani, G. | |
| dc.creator | Takaoka, H. | |
| dc.creator | Tao, T. | |
| dc.date | 2001-10-03 | |
| dc.date | 2001-10-03 | |
| dc.date.accessioned | 2026-07-07T04:43:39Z | |
| dc.date.available | 2026-07-07T04:43:39Z | |
| dc.description | The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all $L^2$-based Sobolev spaces $H^s$ where local well-posedness is presently known, apart from the $H^{1/4} (\R)$ endpoint for mKdV. The result for KdV relies on a new method for constructing almost conserved quantities using multilinear harmonic analysis and the available local-in-time theory. Miura's transformation is used to show that global well-posedness of modified KdV is implied by global well-posedness of the standard KdV equation. | |
| dc.description | submitted to JAMS | |
| dc.identifier | https://arxiv.org/abs/math/0110045 | |
| dc.identifier | http://arxiv.org/abs/math/0110045 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62319 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53, 42B35, 37K10 | |
| dc.title | Sharp Global well-posedness for KdV and modified KdV on $\R$ and $\T$ | |
| dc.type | text |