<?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-02178658</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="2026-05-19T09:19:20+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A homogenized limit for the 2-dimensional Euler equations in a perforated domain</title>
            <author role="aut">
              <persName>
                <forename type="first">Matthieu</forename>
                <surname>Hillairet</surname>
              </persName>
              <email type="md5">eeae0940671412f6bff266aa63e9d9ca</email>
              <email type="domain">umontpellier.fr</email>
              <idno type="idhal" notation="string">matthieu-hillairet</idno>
              <idno type="idhal" notation="numeric">170840</idno>
              <idno type="halauthorid" notation="string">29748-170840</idno>
              <idno type="IDREF">https://www.idref.fr/110248120</idno>
              <affiliation ref="#struct-1100744"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Christophe</forename>
                <surname>Lacave</surname>
              </persName>
              <email type="md5">5ce887f506e86ed05ecd4bab06523ed3</email>
              <email type="domain">univ-smb.fr</email>
              <idno type="idhal" notation="string">christophe-lacave</idno>
              <idno type="idhal" notation="numeric">17838</idno>
              <idno type="halauthorid" notation="string">6644-17838</idno>
              <idno type="ARXIV">https://arxiv.org/a/lacave_c_1</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2488-4117</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?hl=fr&amp;user=sKWU1K8AAAAJ</idno>
              <idno type="IDREF">https://www.idref.fr/131806904</idno>
              <affiliation ref="#struct-1043234"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Di</forename>
                <surname>Wu</surname>
              </persName>
              <email type="md5">66c5f0ae5ec42a5edb0afa9fb8edf6e7</email>
              <email type="domain">163.com</email>
              <idno type="idhal" notation="numeric">1047016</idno>
              <idno type="halauthorid" notation="string">485568-1047016</idno>
              <affiliation ref="#struct-560092"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Christophe</forename>
                <surname>Lacave</surname>
              </persName>
              <email type="md5">5ce887f506e86ed05ecd4bab06523ed3</email>
              <email type="domain">univ-smb.fr</email>
            </editor>
            <funder ref="#projanr-48729"/>
            <funder ref="#projanr-41654"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2019-07-10 09:44:36</date>
              <date type="whenModified">2025-09-27 19:11:57</date>
              <date type="whenReleased">2019-07-10 09:44:36</date>
              <date type="whenProduced">2022</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1907.04131"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="116135">
                <persName>
                  <forename>Christophe</forename>
                  <surname>Lacave</surname>
                </persName>
                <email type="md5">5ce887f506e86ed05ecd4bab06523ed3</email>
                <email type="domain">univ-smb.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02178658</idno>
            <idno type="halUri">https://hal.science/hal-02178658</idno>
            <idno type="halBibtex">hillairet:hal-02178658</idno>
            <idno type="halRefHtml">&lt;i&gt;Analysis &amp; PDE&lt;/i&gt;, 2022, 15 (5), pp.1131-1167. &lt;a target="_blank" href="https://dx.doi.org/10.2140/apde.2022.15.1131"&gt;&amp;#x27E8;10.2140/apde.2022.15.1131&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Analysis &amp; PDE, 2022, 15 (5), pp.1131-1167. &amp;#x27E8;10.2140/apde.2022.15.1131&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UGA">HAL Grenoble Alpes</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="PREPUBIF" corresp="FOURIER">Les prépublications de l'Institut Fourier</idno>
            <idno type="stamp" n="FOURIER">Institut Fourier</idno>
            <idno type="stamp" n="I3M_UMR5149">Institut de Mathématiques et de Modélisation de Montpellier</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IMAG-MONTPELLIER">Institut Montpelliérain Alexander Grothendieck</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-MONTPELLIER">Université de Montpellier</idno>
            <idno type="stamp" n="UGA-EPE">Université Grenoble Alpes [2020-*]</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UM-2015-2021" corresp="UNIV-MONTPELLIER">Université de Montpellier (2015-2021)</idno>
            <idno type="stamp" n="UM-EPE" corresp="UNIV-MONTPELLIER">Université de Montpellier - EPE</idno>
            <idno type="stamp" n="ANR-OCEANS-15TO18" corresp="ANR-OCEANS">ANR-OCEANS-15TO18</idno>
            <idno type="stamp" n="ANR-OCEANS">ANR-OCEANS</idno>
            <idno type="stamp" n="TEST-UGA">TEST-UGA</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">32 pages</note>
            <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">A homogenized limit for the 2-dimensional Euler equations in a perforated domain</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Matthieu</forename>
                    <surname>Hillairet</surname>
                  </persName>
                  <email type="md5">eeae0940671412f6bff266aa63e9d9ca</email>
                  <email type="domain">umontpellier.fr</email>
                  <idno type="idhal" notation="string">matthieu-hillairet</idno>
                  <idno type="idhal" notation="numeric">170840</idno>
                  <idno type="halauthorid" notation="string">29748-170840</idno>
                  <idno type="IDREF">https://www.idref.fr/110248120</idno>
                  <affiliation ref="#struct-1100744"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Christophe</forename>
                    <surname>Lacave</surname>
                  </persName>
                  <email type="md5">5ce887f506e86ed05ecd4bab06523ed3</email>
                  <email type="domain">univ-smb.fr</email>
                  <idno type="idhal" notation="string">christophe-lacave</idno>
                  <idno type="idhal" notation="numeric">17838</idno>
                  <idno type="halauthorid" notation="string">6644-17838</idno>
                  <idno type="ARXIV">https://arxiv.org/a/lacave_c_1</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2488-4117</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?hl=fr&amp;user=sKWU1K8AAAAJ</idno>
                  <idno type="IDREF">https://www.idref.fr/131806904</idno>
                  <affiliation ref="#struct-1043234"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Di</forename>
                    <surname>Wu</surname>
                  </persName>
                  <email type="md5">66c5f0ae5ec42a5edb0afa9fb8edf6e7</email>
                  <email type="domain">163.com</email>
                  <idno type="idhal" notation="numeric">1047016</idno>
                  <idno type="halauthorid" notation="string">485568-1047016</idno>
                  <affiliation ref="#struct-560092"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">PM</idno>
                <idno type="halJournalId" status="VALID">103456</idno>
                <idno type="issn">2157-5045</idno>
                <idno type="eissn">1948-206X</idno>
                <title level="j">Analysis &amp; PDE</title>
                <imprint>
                  <publisher>Mathematical Sciences Publishers</publisher>
                  <biblScope unit="volume">15</biblScope>
                  <biblScope unit="issue">5</biblScope>
                  <biblScope unit="pp">1131-1167</biblScope>
                  <date type="datePub">2022</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1907.04131</idno>
              <idno type="doi">10.2140/apde.2022.15.1131</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>We study the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size $a$ separated by distances $\tilde d$ and the fluid fills the exterior. We analyse the asymptotic behavior of the fluid when $(a,\tilde d) \to (0,0)$. If the inclusions are distributed on the unit square, this issue is studied recently when $\frac{\tilde d}a$ tends to zero or infinity, leaving aside the critical case where the volume fraction of the porous medium is bounded and non-zero. In this paper, we provide the first result in this regime. In contrast with former results, we obtain an Euler type equation where a homogenized term appears in the elliptic problem relating the velocity and the vorticity. Our analysis is based on the so-called method of reflections whose convergence provides novel estimates on the solutions to the div-curl problem which is involved in the 2D-Euler equations.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1100744" status="VALID">
          <idno type="ISNI">0000000404890602</idno>
          <idno type="RNSR">200311827X</idno>
          <idno type="ROR">https://ror.org/044kxby82</idno>
          <orgName>Institut Montpelliérain Alexander Grothendieck</orgName>
          <orgName type="acronym">IMAG</orgName>
          <date type="start">2022-01-01</date>
          <desc>
            <address>
              <addrLine>UMR CNRS 5149 - Université Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5 - France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://imag.umontpellier.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR5149" active="#struct-441569" type="direct"/>
            <relation active="#struct-1100589" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1043234" status="VALID">
          <idno type="IdRef">033629129</idno>
          <idno type="ISNI">0000000122896889</idno>
          <idno type="RNSR">199512018P</idno>
          <idno type="ROR">https://ror.org/05rwrfh97</idno>
          <orgName>Institut Fourier</orgName>
          <orgName type="acronym">IF</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>100, rue des maths 38610 Gières</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-fourier.ujf-grenoble.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR5582" active="#struct-441569" type="direct"/>
            <relation active="#struct-1042703" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-560092" status="VALID">
          <idno type="ROR">https://ror.org/0530pts50</idno>
          <orgName>South China University of Technology [Guangzhou]</orgName>
          <orgName type="acronym">SCUT</orgName>
          <desc>
            <address>
              <addrLine>Guangzhou</addrLine>
              <country key="CN"/>
            </address>
            <ref type="url">https://www.scut.edu.cn/en/</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>
        <org type="regroupinstitution" xml:id="struct-1100589" status="VALID">
          <idno type="ROR">https://ror.org/051escj72</idno>
          <orgName>Université de Montpellier</orgName>
          <orgName type="acronym">UM</orgName>
          <date type="start">2022-01-01</date>
          <desc>
            <address>
              <addrLine>163 rue Auguste Broussonnet - 34090 Montpellier</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.umontpellier.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-1042703" status="VALID">
          <idno type="IdRef">240648315</idno>
          <idno type="ROR">https://ror.org/02rx3b187</idno>
          <orgName>Université Grenoble Alpes</orgName>
          <orgName type="acronym">UGA</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Adresse CS 40700 - 38058 Grenoble cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-grenoble-alpes.fr</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-48729" status="VALID">
          <idno type="anr">ANR-18-CE40-0027</idno>
          <idno type="program">APPEL À PROJETS GÉNÉRIQUE 2018</idno>
          <orgName>SingFlows</orgName>
          <desc>Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure</desc>
          <date type="start">2018</date>
        </org>
        <org type="anrProject" xml:id="projanr-41654" status="VALID">
          <idno type="anr">ANR-15-CE40-0010</idno>
          <idno type="program">Défi de tous les savoirs</idno>
          <orgName>IFSMACS</orgName>
          <desc>Interaction Fluide-Structure : Modélisation, analyse, contrôle et simulation</desc>
          <date type="start">2015</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>