Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane
We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity u sub([infinity]) at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of u sub([infini...
Gespeichert in:
| Veröffentlicht in: | Nonlinearity 2011-06, Vol.24 (6), p.1861-1882, Article 1861 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1882 |
|---|---|
| container_issue | 6 |
| container_start_page | 1861 |
| container_title | Nonlinearity |
| container_volume | 24 |
| creator | Konieczny, P Mucha, P B |
| description | We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity u sub([infinity]) at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of u sub([infinity]) Furthermore a spatial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the direction of the flow as the time direction. The analysis is done in the framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modelled by elliptic equations. |
| doi_str_mv | 10.1088/0951-7715/24/6/010 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_24235034</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1730056859</sourcerecordid><originalsourceid>FETCH-LOGICAL-c426t-853bce169715ce25391257dca5ec0eed8cc1ab0a173dceeed6c9ad474af58dbe3</originalsourceid><addsrcrecordid>eNqNkM1KHUEQhRuJ4M01L-BqNoJZTG7_zs9SNBpBzEKzburW1GDreHvs7hGyyzvkDfMk6fGKC4WQVUHxnVOnDmMHgn8RvGlWvDWirGthVlKvqhUXfIcthKpEWRmtP7DFK7DHPsZ4x7kQjVQL1p26QJic38BQwDgGD3hbJF_EEZLLu5jChGkKVPi-iH6YZjbORLql4gqeHIU_v35fJ39PsaDHCbaA2zwD4wAb2me7PQyRPr3MJftx9vXm5Ft5-f384uT4skQtq1Q2Rq2RRNXmmEjSqFZIU3cIhpATdQ2igDUHUasOKS8qbKHTtYbeNN2a1JIdbX3zG48TxWQfXEQa5gx-ijYLOTdVY9qMyi2KwccYqLdjcA8QflrB7VypnRuzc2NWalvZXGkWHb74Q0QY-gAbdPFVKbVUhiudueaNObr03EsK4IZ_nyi3UufH_4v0-T3_nrNj16u_gFSmDQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1730056859</pqid></control><display><type>article</type><title>Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Konieczny, P ; Mucha, P B</creator><creatorcontrib>Konieczny, P ; Mucha, P B</creatorcontrib><description>We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity u sub([infinity]) at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of u sub([infinity]) Furthermore a spatial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the direction of the flow as the time direction. The analysis is done in the framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modelled by elliptic equations.</description><identifier>ISSN: 0951-7715</identifier><identifier>EISSN: 1361-6544</identifier><identifier>DOI: 10.1088/0951-7715/24/6/010</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Asymptotic properties ; Exact sciences and technology ; Fourier transforms ; Global analysis, analysis on manifolds ; Infinity ; Mathematical analysis ; Mathematical methods in physics ; Mathematical models ; Mathematics ; Navier-Stokes equations ; Other topics in mathematical methods in physics ; Partial differential equations ; Physics ; Planes ; Sciences and techniques of general use ; Special functions ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinearity, 2011-06, Vol.24 (6), p.1861-1882, Article 1861</ispartof><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c426t-853bce169715ce25391257dca5ec0eed8cc1ab0a173dceeed6c9ad474af58dbe3</citedby><cites>FETCH-LOGICAL-c426t-853bce169715ce25391257dca5ec0eed8cc1ab0a173dceeed6c9ad474af58dbe3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/0951-7715/24/6/010/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,780,784,27924,27925,53830,53910</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24235034$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Konieczny, P</creatorcontrib><creatorcontrib>Mucha, P B</creatorcontrib><title>Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane</title><title>Nonlinearity</title><description>We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity u sub([infinity]) at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of u sub([infinity]) Furthermore a spatial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the direction of the flow as the time direction. The analysis is done in the framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modelled by elliptic equations.</description><subject>Asymptotic properties</subject><subject>Exact sciences and technology</subject><subject>Fourier transforms</subject><subject>Global analysis, analysis on manifolds</subject><subject>Infinity</subject><subject>Mathematical analysis</subject><subject>Mathematical methods in physics</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Navier-Stokes equations</subject><subject>Other topics in mathematical methods in physics</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Planes</subject><subject>Sciences and techniques of general use</subject><subject>Special functions</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0951-7715</issn><issn>1361-6544</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNqNkM1KHUEQhRuJ4M01L-BqNoJZTG7_zs9SNBpBzEKzburW1GDreHvs7hGyyzvkDfMk6fGKC4WQVUHxnVOnDmMHgn8RvGlWvDWirGthVlKvqhUXfIcthKpEWRmtP7DFK7DHPsZ4x7kQjVQL1p26QJic38BQwDgGD3hbJF_EEZLLu5jChGkKVPi-iH6YZjbORLql4gqeHIU_v35fJ39PsaDHCbaA2zwD4wAb2me7PQyRPr3MJftx9vXm5Ft5-f384uT4skQtq1Q2Rq2RRNXmmEjSqFZIU3cIhpATdQ2igDUHUasOKS8qbKHTtYbeNN2a1JIdbX3zG48TxWQfXEQa5gx-ijYLOTdVY9qMyi2KwccYqLdjcA8QflrB7VypnRuzc2NWalvZXGkWHb74Q0QY-gAbdPFVKbVUhiudueaNObr03EsK4IZ_nyi3UufH_4v0-T3_nrNj16u_gFSmDQ</recordid><startdate>20110601</startdate><enddate>20110601</enddate><creator>Konieczny, P</creator><creator>Mucha, P B</creator><general>IOP Publishing</general><general>Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20110601</creationdate><title>Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane</title><author>Konieczny, P ; Mucha, P B</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c426t-853bce169715ce25391257dca5ec0eed8cc1ab0a173dceeed6c9ad474af58dbe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Asymptotic properties</topic><topic>Exact sciences and technology</topic><topic>Fourier transforms</topic><topic>Global analysis, analysis on manifolds</topic><topic>Infinity</topic><topic>Mathematical analysis</topic><topic>Mathematical methods in physics</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Navier-Stokes equations</topic><topic>Other topics in mathematical methods in physics</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Planes</topic><topic>Sciences and techniques of general use</topic><topic>Special functions</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Konieczny, P</creatorcontrib><creatorcontrib>Mucha, P B</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Nonlinearity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Konieczny, P</au><au>Mucha, P B</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane</atitle><jtitle>Nonlinearity</jtitle><date>2011-06-01</date><risdate>2011</risdate><volume>24</volume><issue>6</issue><spage>1861</spage><epage>1882</epage><pages>1861-1882</pages><artnum>1861</artnum><issn>0951-7715</issn><eissn>1361-6544</eissn><abstract>We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity u sub([infinity]) at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of u sub([infinity]) Furthermore a spatial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the direction of the flow as the time direction. The analysis is done in the framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modelled by elliptic equations.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/0951-7715/24/6/010</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0951-7715 |
| ispartof | Nonlinearity, 2011-06, Vol.24 (6), p.1861-1882, Article 1861 |
| issn | 0951-7715 1361-6544 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_24235034 |
| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | Asymptotic properties Exact sciences and technology Fourier transforms Global analysis, analysis on manifolds Infinity Mathematical analysis Mathematical methods in physics Mathematical models Mathematics Navier-Stokes equations Other topics in mathematical methods in physics Partial differential equations Physics Planes Sciences and techniques of general use Special functions Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Directional approach to spatial structure of solutions to the Navier–Stokes equations in the plane |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T19%3A30%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Directional%20approach%20to%20spatial%20structure%20of%20solutions%20to%20the%20Navier%E2%80%93Stokes%20equations%20in%20the%20plane&rft.jtitle=Nonlinearity&rft.au=Konieczny,%20P&rft.date=2011-06-01&rft.volume=24&rft.issue=6&rft.spage=1861&rft.epage=1882&rft.pages=1861-1882&rft.artnum=1861&rft.issn=0951-7715&rft.eissn=1361-6544&rft_id=info:doi/10.1088/0951-7715/24/6/010&rft_dat=%3Cproquest_pasca%3E1730056859%3C/proquest_pasca%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1730056859&rft_id=info:pmid/&rfr_iscdi=true |