@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00857679v2> a dcat:Dataset ;
    dct:description """
              Thanks to an approach inspired from Burq-Lebeau \\cite{bule}, we prove stochastic versions of Strichartz estimates for Schrödinger with harmonic potential. As a consequence, we show that the nonlinear Schrödinger equation with quadratic potential and any polynomial non-linearity is almost surely locally well-posed in $L^{2}(\\R^{d})$ for any $d\\geq 2$. Then, we show that we can combine this result with the high-low frequency decomposition method of Bourgain to prove a.s. global well-posedness results for the cubic equation: when $d=2$, we prove global well-posedness in $\\H^{s}(\\R^{2})$ for any $s>0$, and when $d=3$ we prove global well-posedness in $\\H^{s}(\\R^{3})$ for any $s>1/6$, which is a supercritical regime. Furthermore, we also obtain almost sure global well-posedness results with scattering for NLS on $\\R^{d}$ without potential. We prove scattering results for $L^2-$supercritical equations and $L^2-$subcritical equations with initial conditions in $L^2$ without additional decay or regularity assumption.
            """ ;
    dct:identifier "hal-00857679" ;
    dct:issued "2026-05-05T11:48:33.841709"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-05T11:48:33.841714"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Probabilistic global well-posedness for the supercritical nonlinear harmonic oscillator" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00857679v2/resource/e8b7471a-406d-4afa-b69c-590424d06a00> ;
    dcat:keyword "35q55--35r60--35p05",
        "global-solutions",
        "harmonic-oscillator",
        "infoeu-reposemanticsarticle",
        "journal-articles",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "mathmath-camathematics-mathclassical-analysis-and-odes-mathca",
        "mathmath-mpmathematics-mathmathematical-physics-math-ph",
        "mathmath-spmathematics-mathspectral-theory-mathsp",
        "random-initial-conditions",
        "scattering",
        "supercritical-non-linear-schrodinger-equation" ;
    dcat:landingPage <ISSN:%202157-5045> .

<ISSN:%202157-5045> a foaf:Document .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00857679v2/resource/e8b7471a-406d-4afa-b69c-590424d06a00> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-05T11:48:33.844352"^^xsd:dateTime ;
    dct:modified "2026-05-05T11:48:33.829432"^^xsd:dateTime ;
    dct:title "Probabilistic global well-posedness for the supercritical nonlinear harmonic oscillator" ;
    dcat:accessURL <https://hal.science/hal-00857679> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .