On the local well-posedness for some systems of coupled KdV equations
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ALVAREZ-SAMANIEGO, Borys | |
| hal.structure.identifier | Instituto de Matemática, Estatística e Computação Científica [Brésil] [IMECC] | |
| dc.contributor.author | CARVAJAL, Xavier | |
| dc.date.accessioned | 2024-04-04T03:11:28Z | |
| dc.date.available | 2024-04-04T03:11:28Z | |
| dc.date.created | 2007-05-03 | |
| dc.date.issued | 2008-07-15 | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193780 | |
| dc.description.abstractEn | Using 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.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | On the local well-posedness for some systems of coupled KdV equations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.na.2007.06.009 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 0705.0482 | |
| bordeaux.journal | Nonlinear Analysis: Theory, Methods and Applications | |
| bordeaux.page | 692 - 715 | |
| bordeaux.volume | 69 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 02 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00144594 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00144594v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Nonlinear%20Analysis:%20Theory,%20Methods%20and%20Applications&rft.date=2008-07-15&rft.volume=69&rft.issue=02&rft.spage=692%20-%20715&rft.epage=692%20-%20715&rft.eissn=0362-546X&rft.issn=0362-546X&rft.au=ALVAREZ-SAMANIEGO,%20Borys&CARVAJAL,%20Xavier&rft.genre=article |
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