Rough solutions for the periodic Schrödinger - Kortweg-deVries system

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dc.creatorArbieto, Alexander
dc.creatorCorcho, Adan
dc.creatorMatheus, Carlos
dc.date2005-11-19
dc.date.accessioned2026-07-07T06:51:29Z
dc.date.available2026-07-07T06:51:29Z
dc.descriptionWe prove two new mixed sharp bilinear estimates of Schrödinger-Airy type. In particular, we obtain the local well-posedness of the Cauchy problem of the Schrödinger - Kortweg-deVries (NLS-KdV) system in the \emph{periodic setting}. Our lowest regularity is $H^{1/4}\times L^2$, which is somewhat far from the naturally expected endpoint $L^2\times H^{-1/2}$. This is a novel phenomena related to the periodicity condition. Indeed, in the continuous case, Corcho and Linares proved local well-posedness for the natural endpoint $L^2\times H^{-{3/4}+}$. Nevertheless, we conclude the global well-posedness of the NLS-KdV system in the energy space $H^1\times H^1$ using our local well-posedness result and three conservation laws discovered by M. Tsutsumi.
dc.identifierhttps://arxiv.org/abs/math/0511491
dc.identifierhttp://arxiv.org/abs/math/0511491
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105001
dc.subjectAnalysis of PDEs
dc.subject35Q99
dc.titleRough solutions for the periodic Schrödinger - Kortweg-deVries system
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