<?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-01701332</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="2026-05-15T17:43:00+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Constantin and Iyer’s representation formula for the Navier–Stokes equations on manifolds</title>
            <author role="aut">
              <persName>
                <forename type="first">Shizan</forename>
                <surname>Fang</surname>
              </persName>
              <email type="md5">c0ebe72c8a3d61106ed5683e5ea55ae2</email>
              <email type="domain">u-bourgogne.fr</email>
              <idno type="idhal" notation="numeric">828629</idno>
              <idno type="halauthorid" notation="string">56723-828629</idno>
              <affiliation ref="#struct-50"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Dejun</forename>
                <surname>Luo</surname>
              </persName>
              <email type="md5">d0b60101913a55cbc3372e2ec3cfb6d2</email>
              <email type="domain">amss.ac.cn</email>
              <idno type="idhal" notation="numeric">1037587</idno>
              <idno type="halauthorid" notation="string">938181-1037587</idno>
              <affiliation ref="#struct-527447"/>
              <affiliation ref="#struct-527449"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>IMB -</forename>
                <surname>université de Bourgogne</surname>
              </persName>
              <email type="md5">037b53e891a987261daa89c229598704</email>
              <email type="domain">u-bourgogne.fr</email>
            </editor>
            <funder>National Natural Science Foundation of China. Grant number: 11431014, 11571347</funder>
            <funder>Seven Main Directions. Grant number: Y129161ZZ1</funder>
            <funder>Academy of Mathematics and Systems Science, Chinese Academy of Sciences</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2018-02-05 16:54:22</date>
              <date type="whenModified">2025-03-31 08:12:05</date>
              <date type="whenReleased">2018-02-05 16:54:22</date>
              <date type="whenProduced">2018-02</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1508.06387"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="456684">
                <persName>
                  <forename>IMB -</forename>
                  <surname>université de Bourgogne</surname>
                </persName>
                <email type="md5">037b53e891a987261daa89c229598704</email>
                <email type="domain">u-bourgogne.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01701332</idno>
            <idno type="halUri">https://hal.science/hal-01701332</idno>
            <idno type="halBibtex">fang:hal-01701332</idno>
            <idno type="halRefHtml">&lt;i&gt;Potential Analysis&lt;/i&gt;, 2018, 48 (2), pp.181-206. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s11118-017-9631-0"&gt;&amp;#x27E8;10.1007/s11118-017-9631-0&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Potential Analysis, 2018, 48 (2), pp.181-206. &amp;#x27E8;10.1007/s11118-017-9631-0&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-BOURGOGNE">Université Bourgogne Europe</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IMB_UMR5584" corresp="UNIV-BOURGOGNE">Institut de Mathématiques de Bourgogne</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">Constantin and Iyer’s representation formula for the Navier–Stokes equations on manifolds</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Shizan</forename>
                    <surname>Fang</surname>
                  </persName>
                  <email type="md5">c0ebe72c8a3d61106ed5683e5ea55ae2</email>
                  <email type="domain">u-bourgogne.fr</email>
                  <idno type="idhal" notation="numeric">828629</idno>
                  <idno type="halauthorid" notation="string">56723-828629</idno>
                  <affiliation ref="#struct-50"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Dejun</forename>
                    <surname>Luo</surname>
                  </persName>
                  <email type="md5">d0b60101913a55cbc3372e2ec3cfb6d2</email>
                  <email type="domain">amss.ac.cn</email>
                  <idno type="idhal" notation="numeric">1037587</idno>
                  <idno type="halauthorid" notation="string">938181-1037587</idno>
                  <affiliation ref="#struct-527447"/>
                  <affiliation ref="#struct-527449"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">18147</idno>
                <idno type="issn">0926-2601</idno>
                <idno type="eissn">1572-929X</idno>
                <title level="j">Potential Analysis</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">48</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">181–206</biblScope>
                  <date type="datePub">2018-02</date>
                  <date type="dateEpub">2017-06-02</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1508.06387</idno>
              <idno type="doi">10.1007/s11118-017-9631-0</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Pull-back vector field</term>
                <term xml:lang="en">Stochastic flow</term>
                <term xml:lang="en">Navier–Stokes equations</term>
                <term xml:lang="en">de Rham–Hodge Laplacian</term>
                <term xml:lang="en">Stochastic representation</term>
              </keywords>
              <classCode scheme="classification">MSC: 35Q30, 58J65</classCode>
              <classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</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 purpose of this paper is to establish a probabilistic representation formula for the Navier--Stokes equations on compact Riemannian manifolds. Such a formula has been provided by Constantin and Iyer in the flat case of $\mathbb R^n$ or of $\mathbb T^n$. On a Riemannian manifold, however, there are several different choices of Laplacian operators acting on vector fields. In this paper, we shall use the de Rham--Hodge Laplacian operator which seems more relevant to the probabilistic setting, and adopt Elworthy--Le Jan--Li's idea to decompose it as a sum of the square of Lie derivatives.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-50" status="OLD">
          <idno type="IdRef">159771242</idno>
          <idno type="ISNI">0000000403844815</idno>
          <idno type="RNSR">199512020S</idno>
          <idno type="ROR">https://ror.org/021f0sa24</idno>
          <orgName>Institut de Mathématiques de Bourgogne [Dijon]</orgName>
          <orgName type="acronym">IMB</orgName>
          <date type="start">2015-01-01</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>Université de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.u-bourgogne.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300270" type="direct"/>
            <relation name="UMR5584" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-527447" status="INCOMING">
          <orgName>Key Laboratory of Random Complex Structures and Data Sciences [Beijing]</orgName>
          <desc>
            <address>
              <country key="CN"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-301741" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-527449" status="INCOMING">
          <orgName>School of Mathematical Sciences [Beijing]</orgName>
          <desc>
            <address>
              <country key="CN"/>
            </address>
            <ref type="url">http://math.ucas.ac.cn/index.php/en/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-469160" type="direct"/>
            <relation active="#struct-303369" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300270" status="OLD">
          <idno type="IdRef">02819005X</idno>
          <idno type="ISNI">0000000122989313</idno>
          <idno type="ROR">https://ror.org/03k1bsr36</idno>
          <orgName>Université de Bourgogne</orgName>
          <orgName type="acronym">UB</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>Maison de l'université - Esplanade Érasme - BP 27877 - 21078 Dijon cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-bourgogne.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>
        <org type="institution" xml:id="struct-301741" status="VALID">
          <idno type="ROR">https://ror.org/02jkmyk67</idno>
          <orgName>Academy of Mathematics and Systems Science [Beijing]</orgName>
          <desc>
            <address>
              <addrLine>Beijing 100190</addrLine>
              <country key="CN"/>
            </address>
            <ref type="url">http://english.amss.cas.cn/</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-469160" status="VALID">
          <idno type="ROR">https://ror.org/05qbk4x57</idno>
          <orgName>University of Chinese Academy of Sciences [Beijing]</orgName>
          <orgName type="acronym">UCAS</orgName>
          <date type="start">2016-10-20</date>
          <desc>
            <address>
              <addrLine>No.19(A) Yuquan Road, Shijingshan District, Beijing, P.R.China 100049</addrLine>
              <country key="CN"/>
            </address>
            <ref type="url">http://english.ucas.ac.cn/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-303369" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-303369" status="VALID">
          <idno type="ROR">https://ror.org/034t30j35</idno>
          <orgName>Chinese Academy of Sciences [Beijing]</orgName>
          <orgName type="acronym">CAS</orgName>
          <desc>
            <address>
              <addrLine>52 Sanlihe Rd., Beijing, 100864</addrLine>
              <country key="CN"/>
            </address>
            <ref type="url">http://english.cas.cn/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>