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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorALVAREZ-SAMANIEGO, Borys
hal.structure.identifierInstituto de Matemática, Estatística e Computação Científica [Brésil] [IMECC]
dc.contributor.authorCARVAJAL, Xavier
dc.date.accessioned2024-04-04T03:11:28Z
dc.date.available2024-04-04T03:11:28Z
dc.date.created2007-05-03
dc.date.issued2008-07-15
dc.identifier.issn0362-546X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193780
dc.description.abstractEnUsing the theory developed by Kenig, Ponce, and Vega, we prove that the Hirota-Satsuma system is locally well-posed in Sobolev spaces $H^s(\mathbb{R}) \times H^{s}(\mathbb{R})$ for $3/4< s \le 1$. We introduce some Bourgain-type spaces $X_{s,b}^a$ for $a\not =0$, $s,b \in \mathbb{R}$ to obtain local well-posedness for the Gear-Grimshaw system in $H^s(\mathbb{R})\times H^s(\mathbb{R})$ for $s>-3/4$, by establishing new mixed-bilinear estimates involving the two Bourgain-type spaces $X_{s,b}^{-\alpha_-}$ and $X_{s,b}^{-\alpha_+}$ adapted to $\partial_t+\alpha_-\partial_x^3$ and $\partial_t+\alpha_+\partial_x^3$ respectively, where $|\alpha_+|=|\alpha_-|\not = 0$.
dc.language.isoen
dc.publisherElsevier
dc.title.enOn the local well-posedness for some systems of coupled KdV equations
dc.typeArticle de revue
dc.identifier.doi10.1016/j.na.2007.06.009
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv0705.0482
bordeaux.journalNonlinear Analysis: Theory, Methods and Applications
bordeaux.page692 - 715
bordeaux.volume69
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue02
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00144594
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00144594v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Nonlinear%20Analysis:%20Theory,%20Methods%20and%20Applications&amp;rft.date=2008-07-15&amp;rft.volume=69&amp;rft.issue=02&amp;rft.spage=692%20-%20715&amp;rft.epage=692%20-%20715&amp;rft.eissn=0362-546X&amp;rft.issn=0362-546X&amp;rft.au=ALVAREZ-SAMANIEGO,%20Borys&amp;CARVAJAL,%20Xavier&amp;rft.genre=article


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