<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01523517</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-09T00:02:20+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Small Data Solutions of the Vlasov-Poisson System and the Vector Field Method</title>
            <author role="aut">
              <persName>
                <forename type="first">Jacques</forename>
                <surname>Smulevici</surname>
              </persName>
              <email type="md5">b0ee1bd082dbf5d28fc154ca97884f20</email>
              <email type="domain">math.u-psud.fr</email>
              <idno type="idhal" notation="numeric">913227</idno>
              <idno type="halauthorid" notation="string">594395-913227</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0671-4656</idno>
              <idno type="IDREF">https://www.idref.fr/188802797</idno>
              <affiliation ref="#struct-40"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jacques</forename>
                <surname>Smulevici</surname>
              </persName>
              <email type="md5">1e5a318aed0f689be4d212b9e2785a60</email>
              <email type="domain">upmc.fr</email>
            </editor>
            <funder ref="#projanr-35058"/>
            <funder ref="#projanr-33705"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2017-05-16 14:09:40</date>
              <date type="whenModified">2026-02-07 05:13:42</date>
              <date type="whenReleased">2017-05-16 14:09:40</date>
              <date type="whenProduced">2016-12-16</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1504.02195"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="166418">
                <persName>
                  <forename>Jacques</forename>
                  <surname>Smulevici</surname>
                </persName>
                <email type="md5">1e5a318aed0f689be4d212b9e2785a60</email>
                <email type="domain">upmc.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01523517</idno>
            <idno type="halUri">https://hal.science/hal-01523517</idno>
            <idno type="halBibtex">smulevici:hal-01523517</idno>
            <idno type="halRefHtml">&lt;i&gt;Annals of PDE&lt;/i&gt;, 2016, &lt;a target="_blank" href="https://dx.doi.org/10.1007/s40818-016-0016-2"&gt;&amp;#x27E8;10.1007/s40818-016-0016-2&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Annals of PDE, 2016, &amp;#x27E8;10.1007/s40818-016-0016-2&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="LM-ORSAY">Laboratoire de Mathématiques d'Orsay</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-PSUD-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris Sud pour Paris Saclay</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="GS-MATHEMATIQUES">Graduate School Mathématiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Small Data Solutions of the Vlasov-Poisson System and the Vector Field Method</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Jacques</forename>
                    <surname>Smulevici</surname>
                  </persName>
                  <email type="md5">b0ee1bd082dbf5d28fc154ca97884f20</email>
                  <email type="domain">math.u-psud.fr</email>
                  <idno type="idhal" notation="numeric">913227</idno>
                  <idno type="halauthorid" notation="string">594395-913227</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0671-4656</idno>
                  <idno type="IDREF">https://www.idref.fr/188802797</idno>
                  <affiliation ref="#struct-40"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">117393</idno>
                <idno type="issn">2524-5317</idno>
                <idno type="eissn">2199-2576</idno>
                <title level="j">Annals of PDE</title>
                <imprint>
                  <publisher>Springer</publisher>
                  <date type="datePub">2016-12-16</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1504.02195</idno>
              <idno type="doi">10.1007/s40818-016-0016-2</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>The aim of this article is to demonstrate how the vector field method of Klainerman can be adapted to the study of transport equations. After an illustration of the method for the free transport operator, we apply the vector field method to the Vlasov-Poisson system in dimension 3 or greater. The main results are optimal decay estimates and the propagation of global bounds for commuted fields associated with the conservation laws of the free transport operators, under some smallness assumption. Similar decay estimates had been obtained previously by Hwang, Rendall and Velázquez using the method of characteristics, but the results presented here are the first to contain the global bounds for commuted fields and the optimal spatial decay estimates. In dimension 4 or greater, it suffices to use the standard vector fields commuting with the free transport operator while in dimension 3, the rate of decay is such that these vector fields would generate a logarithmic loss. Instead, we construct modified vector fields where the modification depends on the solution itself. The methods of this paper, being based on commutation vector fields and conservation laws, are applicable in principle to a wide range of systems, including the Einstein-Vlasov and the Vlasov-Nordström system.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-40" status="OLD">
          <orgName>Laboratoire de Mathématiques d'Orsay</orgName>
          <orgName type="acronym">LMO</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 307, rue Michel Magat, Faculté des sciences, Université Paris-Saclay, 91405 Orsay Cédex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.u-psud.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
            <relation name="UMR8628" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92966" status="OLD">
          <idno type="ROR">https://ror.org/028rypz17</idno>
          <orgName>Université Paris-Sud - Paris 11</orgName>
          <orgName type="acronym">UP11</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-psud.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-35058" status="VALID">
          <idno type="anr">ANR-12-BS01-0012</idno>
          <idno type="program">BLANC</idno>
          <orgName>AARG</orgName>
          <desc>Analyse Asymptotique en Relativité Générale</desc>
          <date type="start">2012</date>
        </org>
        <org type="anrProject" xml:id="projanr-33705" status="VALID">
          <idno type="anr">ANR-11-BS01-0003</idno>
          <idno type="program">BLANC</idno>
          <orgName>GR-Analysis-Geometry</orgName>
          <desc>Relativité Générale Mathématique. Analyse et géométrie des espaces-temps peu réguliers</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>