Existence and uniqueness of time-periodic physically reasonable Navier-Stokes flow past a body
Let Ω be a three-dimensional exterior domain of class C^sup 2,α^ , 0
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Veröffentlicht in: | Archive for rational mechanics and analysis 2004-05, Vol.172 (3), p.363-406 |
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creator | GALDI, Giovanni P SOHR, Hermann |
description | Let Ω be a three-dimensional exterior domain of class C^sup 2,α^ , 0 |
doi_str_mv | 10.1007/s00205-004-0306-9 |
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Assume that a Navier-Stokes liquid is moving in Ω under the action of a body force F that is time-periodic of period T , and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x | as |x |^sup -1^ and its spatial gradient decays as |x |^sup -2^ , both uniformly in time. In addition, the pressure p decays like |x |^sup -2^ and its gradient like |x |^sup -3^ , for almost all t [0,T ]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finn's ''physically reasonable'' solutions [4]. Moreover, we show that our time-periodic solutions are unique in a very large class, namely, the class of time-periodic weak solutions satisfying the ''energy inequality'' and with corresponding pressure fields verifying mild summability conditions in Ω×[0,T ].[PUBLICATION ABSTRACT]</description><identifier>ISSN: 0003-9527</identifier><identifier>EISSN: 1432-0673</identifier><identifier>DOI: 10.1007/s00205-004-0306-9</identifier><identifier>CODEN: AVRMAW</identifier><language>eng</language><publisher>Heidelberg: Springer</publisher><subject>Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Mathematical methods in physics ; Numerical approximation and analysis ; Ordinary and partial differential equations, boundary value problems ; Physics ; Studies</subject><ispartof>Archive for rational mechanics and analysis, 2004-05, Vol.172 (3), p.363-406</ispartof><rights>2004 INIST-CNRS</rights><rights>Springer-Verlag Berlin Heidelberg 2004</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c300t-837264ef6a2f0e1aafee5404c93c5bfe26c1836dc133e8047eeb5c9feb14daf03</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15804413$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>GALDI, Giovanni P</creatorcontrib><creatorcontrib>SOHR, Hermann</creatorcontrib><title>Existence and uniqueness of time-periodic physically reasonable Navier-Stokes flow past a body</title><title>Archive for rational mechanics and analysis</title><description>Let Ω be a three-dimensional exterior domain of class C^sup 2,α^ , 0<α<1. Assume that a Navier-Stokes liquid is moving in Ω under the action of a body force F that is time-periodic of period T , and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x | as |x |^sup -1^ and its spatial gradient decays as |x |^sup -2^ , both uniformly in time. In addition, the pressure p decays like |x |^sup -2^ and its gradient like |x |^sup -3^ , for almost all t [0,T ]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finn's ''physically reasonable'' solutions [4]. Moreover, we show that our time-periodic solutions are unique in a very large class, namely, the class of time-periodic weak solutions satisfying the ''energy inequality'' and with corresponding pressure fields verifying mild summability conditions in Ω×[0,T ].[PUBLICATION ABSTRACT]</description><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Mathematical methods in physics</subject><subject>Numerical approximation and analysis</subject><subject>Ordinary and partial differential equations, boundary value problems</subject><subject>Physics</subject><subject>Studies</subject><issn>0003-9527</issn><issn>1432-0673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNpFkE9LxDAQxYMouK5-AG9B8BidNGnaHmXxHyx6UK-GNJ1g1m5Tk67ab2-XXfA0DLz35s2PkHMOVxyguE4AGeQMQDIQoFh1QGZcioyBKsQhmQGAYFWeFcfkJKXVds2EmpH321-fBuwsUtM1dNP5rw12mBINjg5-jazH6EPjLe0_xuStaduRRjQpdKZukT6Zb4-RvQzhExN1bfihvUkDNbQOzXhKjpxpE57t55y83d2-Lh7Y8vn-cXGzZFYADKwURaYkOmUyB8iNcYi5BGkrYfPaYaYsL4VqLBcCS5AFYp3bymHNZWMciDm52OX2MUwPpEGvwiZ200ldVqLIZaW2Ir4T2RhSiuh0H_3axFFz0FuKekdRTxT1lqKuJs_lPtik6XcXTWd9-jfmUxs5tfoDz-BzYw</recordid><startdate>20040501</startdate><enddate>20040501</enddate><creator>GALDI, Giovanni P</creator><creator>SOHR, Hermann</creator><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20040501</creationdate><title>Existence and uniqueness of time-periodic physically reasonable Navier-Stokes flow past a body</title><author>GALDI, Giovanni P ; 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Assume that a Navier-Stokes liquid is moving in Ω under the action of a body force F that is time-periodic of period T , and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x | as |x |^sup -1^ and its spatial gradient decays as |x |^sup -2^ , both uniformly in time. In addition, the pressure p decays like |x |^sup -2^ and its gradient like |x |^sup -3^ , for almost all t [0,T ]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finn's ''physically reasonable'' solutions [4]. Moreover, we show that our time-periodic solutions are unique in a very large class, namely, the class of time-periodic weak solutions satisfying the ''energy inequality'' and with corresponding pressure fields verifying mild summability conditions in Ω×[0,T ].[PUBLICATION ABSTRACT]</abstract><cop>Heidelberg</cop><cop>Berlin</cop><cop>New York, NY</cop><pub>Springer</pub><doi>10.1007/s00205-004-0306-9</doi><tpages>44</tpages></addata></record> |
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subjects | Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical methods in physics Numerical approximation and analysis Ordinary and partial differential equations, boundary value problems Physics Studies |
title | Existence and uniqueness of time-periodic physically reasonable Navier-Stokes flow past a body |
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