|
|||||
|
|
Sharp global well-posedness for KdV and modified KdV on |
|
| Authors: | J. Colliander M. Keel G. Staffilani H. Takaoka T. Tao |
| Affiliation: | Department of Mathematics, University of Toronto, Toronto, ON Canada, M5S 3G3 M. Keel ; School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455 G. Staffilani ; Department of Mathematics, Stanford University, Stanford, California 94305-2125 ; Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan ; Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555 |
| Abstract: | 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  -based Sobolev spaces  where local well-posedness is presently known, apart from the  endpoint for mKdV and the  endpoint for KdV. 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. |
| Keywords: | Korteweg-de Vries equation nonlinear dispersive equations bilinear estimates multilinear harmonic analysis |
| 点击此处可从《Journal of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Journal of the American Mathematical Society》下载全文 | |