A remark on normal forms and the "upside-down" I-method for periodic NLS: Growth of higher Sobolev norms

Cited 22 time in webofscience Cited 0 time in scopus
  • Hit : 1192
  • Download : 0
DC FieldValueLanguage
dc.contributor.authorColliander, Jamesko
dc.contributor.authorKwon, Soonsikko
dc.contributor.authorOh, Tadahiroko
dc.date.accessioned2013-03-13T03:51:10Z-
dc.date.available2013-03-13T03:51:10Z-
dc.date.created2012-12-24-
dc.date.created2012-12-24-
dc.date.created2012-12-24-
dc.date.issued2012-10-
dc.identifier.citationJOURNAL D ANALYSE MATHEMATIQUE, v.118, pp.55 - 82-
dc.identifier.issn0021-7670-
dc.identifier.urihttp://hdl.handle.net/10203/104407-
dc.description.abstractWe 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.languageEnglish-
dc.publisherSPRINGER-
dc.titleA remark on normal forms and the "upside-down" I-method for periodic NLS: Growth of higher Sobolev norms-
dc.typeArticle-
dc.identifier.wosid000310836400003-
dc.identifier.scopusid2-s2.0-84869062187-
dc.type.rimsART-
dc.citation.volume118-
dc.citation.beginningpage55-
dc.citation.endingpage82-
dc.citation.publicationnameJOURNAL D ANALYSE MATHEMATIQUE-
dc.identifier.doi10.1007/s11854-012-0029-z-
dc.contributor.localauthorKwon, Soonsik-
dc.contributor.nonIdAuthorColliander, James-
dc.contributor.nonIdAuthorOh, Tadahiro-
dc.type.journalArticleArticle-
dc.subject.keywordPlusNONLINEAR SCHRODINGER-EQUATION-
dc.subject.keywordPlusBOUNDS-
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 22 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0