Global well-posedness for KdV in Sobolev spaces of negative index
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in $H^s(mathbb{R})$ for $-3/10<s$.
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2001-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2001/26/abstr.html |
| _version_ | 1818757073401282560 |
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| author | James Colliander M. Keel Gigliola Staffilani Hideo Takaoka T. Tao |
| author_facet | James Colliander M. Keel Gigliola Staffilani Hideo Takaoka T. Tao |
| author_sort | James Colliander |
| collection | DOAJ |
| description | The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in $H^s(mathbb{R})$ for $-3/10<s$. |
| first_indexed | 2024-12-18T06:05:08Z |
| format | Article |
| id | doaj.art-88a4613f7964440a9edb37812e51688a |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T06:05:08Z |
| publishDate | 2001-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-88a4613f7964440a9edb37812e51688a2022-12-21T21:18:34ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912001-04-0120012617Global well-posedness for KdV in Sobolev spaces of negative indexJames CollianderM. KeelGigliola StaffilaniHideo TakaokaT. TaoThe initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in $H^s(mathbb{R})$ for $-3/10<s$.http://ejde.math.txstate.edu/Volumes/2001/26/abstr.htmlKorteweg-de Vries equationnonlinear dispersive equationsbilinear estimates. |
| spellingShingle | James Colliander M. Keel Gigliola Staffilani Hideo Takaoka T. Tao Global well-posedness for KdV in Sobolev spaces of negative index Electronic Journal of Differential Equations Korteweg-de Vries equation nonlinear dispersive equations bilinear estimates. |
| title | Global well-posedness for KdV in Sobolev spaces of negative index |
| title_full | Global well-posedness for KdV in Sobolev spaces of negative index |
| title_fullStr | Global well-posedness for KdV in Sobolev spaces of negative index |
| title_full_unstemmed | Global well-posedness for KdV in Sobolev spaces of negative index |
| title_short | Global well-posedness for KdV in Sobolev spaces of negative index |
| title_sort | global well posedness for kdv in sobolev spaces of negative index |
| topic | Korteweg-de Vries equation nonlinear dispersive equations bilinear estimates. |
| url | http://ejde.math.txstate.edu/Volumes/2001/26/abstr.html |
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