DC Field | Value | Language |
---|---|---|
dc.contributor.author | Colliander, James | ko |
dc.contributor.author | Kwon, Soonsik | ko |
dc.contributor.author | Oh, Tadahiro | ko |
dc.date.accessioned | 2013-03-13T03:51:10Z | - |
dc.date.available | 2013-03-13T03:51:10Z | - |
dc.date.created | 2012-12-24 | - |
dc.date.created | 2012-12-24 | - |
dc.date.created | 2012-12-24 | - |
dc.date.issued | 2012-10 | - |
dc.identifier.citation | JOURNAL D ANALYSE MATHEMATIQUE, v.118, pp.55 - 82 | - |
dc.identifier.issn | 0021-7670 | - |
dc.identifier.uri | http://hdl.handle.net/10203/104407 | - |
dc.description.abstract | We study growth of higher Sobolev norms of solutions of the onedimensional periodic nonlinear Schrodinger equation (NLS). By a combination of the normal form reduction and the upside-down I-method, we establish parallel to u(t)parallel to H-s less than or similar to(1+vertical bar t vertical bar)(alpha(s-1)+) with alpha = 1 for a general power nonlinearity. In the quintic case, we obtain the above estimate with alpha = 1/2 via the space-time estimate due to Bourgain [4, 5]. In the cubic case, we compute concretely the terms arising in the first few steps of the normal form reduction and prove the above estimate with alpha = 4/9. These results improve the previously known results (except for the quintic case). In the Appendix, we also show how Bourgain's idea in [4] on the normal form reduction for the quintic nonlinearity can be applied to other powers. | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.title | A remark on normal forms and the "upside-down" I-method for periodic NLS: Growth of higher Sobolev norms | - |
dc.type | Article | - |
dc.identifier.wosid | 000310836400003 | - |
dc.identifier.scopusid | 2-s2.0-84869062187 | - |
dc.type.rims | ART | - |
dc.citation.volume | 118 | - |
dc.citation.beginningpage | 55 | - |
dc.citation.endingpage | 82 | - |
dc.citation.publicationname | JOURNAL D ANALYSE MATHEMATIQUE | - |
dc.identifier.doi | 10.1007/s11854-012-0029-z | - |
dc.contributor.localauthor | Kwon, Soonsik | - |
dc.contributor.nonIdAuthor | Colliander, James | - |
dc.contributor.nonIdAuthor | Oh, Tadahiro | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | NONLINEAR SCHRODINGER-EQUATION | - |
dc.subject.keywordPlus | BOUNDS | - |
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