On Unconditional Well-Posedness of Modified KdV

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dc.contributor.authorKwon, Soonsikko
dc.contributor.authorOh, Tadahiroko
dc.date.accessioned2013-03-13T00:18:11Z-
dc.date.available2013-03-13T00:18:11Z-
dc.date.created2012-09-27-
dc.date.created2012-09-27-
dc.date.created2012-09-27-
dc.date.issued2012-08-
dc.identifier.citationINTERNATIONAL MATHEMATICS RESEARCH NOTICES, v.2012, no.15, pp.3509 - 3534-
dc.identifier.issn1073-7928-
dc.identifier.urihttp://hdl.handle.net/10203/103987-
dc.description.abstractBourgain [2] proved that the periodic modified Korteweg-de Vries (mKdV) equation is locally well-posed in H-s(T), s >= 1/2, by introducing new weighted Sobolev spaces X-s,X-b, where the uniqueness holds conditionally, namely in C([0, T]; H-s) boolean AND X-s,X-1/2 ([0, T] x T). In this paper, we establish unconditional well-posedness of mKdV in H-s(T), s >= 1/2, that is, in addition we establish unconditional uniqueness in C([0, T]; H-s), s >= 1/2, of solutions to mKdV. We prove this result via differentiation by parts. For the endpoint case s = 1/2, we perform careful quinti- and septi-linear estimates after the second differentiation by parts.-
dc.languageEnglish-
dc.publisherOXFORD UNIV PRESS-
dc.titleOn Unconditional Well-Posedness of Modified KdV-
dc.typeArticle-
dc.identifier.wosid000307173400006-
dc.identifier.scopusid2-s2.0-84864681131-
dc.type.rimsART-
dc.citation.volume2012-
dc.citation.issue15-
dc.citation.beginningpage3509-
dc.citation.endingpage3534-
dc.citation.publicationnameINTERNATIONAL MATHEMATICS RESEARCH NOTICES-
dc.identifier.doi10.1093/imrn/rnr156-
dc.contributor.localauthorKwon, Soonsik-
dc.contributor.nonIdAuthorOh, Tadahiro-
dc.type.journalArticleArticle-
dc.subject.keywordPlusH-S-
dc.subject.keywordPlusEQUATION-
dc.subject.keywordPlusSCHRODINGER-
dc.subject.keywordPlusUNIQUENESS-
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