On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification

On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification

In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the as...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Acta mathematica scientia 2023-05, Vol.43 (3), p.1081-1104
Hauptverfasser: Pu, Xueke, Zhou, Wenli
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1104
container_issue 3
container_start_page 1081
container_title Acta mathematica scientia
container_volume 43
creator Pu, Xueke
Zhou, Wenli
description In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.
doi_str_mv 10.1007/s10473-023-0306-1
format Article
fullrecord <record><control><sourceid>wanfang_jour_cross</sourceid><recordid>TN_cdi_wanfang_journals_sxwlxb_e202303006</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><wanfj_id>sxwlxb_e202303006</wanfj_id><sourcerecordid>sxwlxb_e202303006</sourcerecordid><originalsourceid>FETCH-LOGICAL-c274t-6a731d5c447f52e553ee46064dee547f6e5a216976cdebf6b4ee8023b64e35713</originalsourceid><addsrcrecordid>eNp1kElPwzAQhS0EEqXwA7j5yiFgO17aIyplkYqK2K6Wk05SV20Cdrr9eyYNEicOlsfj773RPEIuObvmjJmbyJk0acIEnpTphB-RHldGJEM2MMekx4TCWjNxSs5iXDDGtdCyR8ppRZs50Fdf1qFeR_rs8Llyjc_dkt5B8Bus64oWdTiAnz7mLfcS_Mo3fgN0_L0-IJFufTNHTRV9s6dvTcB2gT7t5zk5KdwywsXv3Scf9-P30WMymT48jW4nSS6MbBLtTMpnKpfSFEqAUimA1EzLGYDCngblBNdDo_MZZIXOJMAAl860hFQZnvbJVee7dVXhqtIu6nWocKKNu-1yl1kQiGNETCPLOzYPdYwBCvuFS7mwt5zZNlXbpWpRYdtUbesvOk1Etioh_A34X_QD53J7rQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification</title><source>SpringerNature Journals</source><source>Alma/SFX Local Collection</source><creator>Pu, Xueke ; Zhou, Wenli</creator><creatorcontrib>Pu, Xueke ; Zhou, Wenli</creatorcontrib><description>In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.</description><identifier>ISSN: 0252-9602</identifier><identifier>EISSN: 1572-9087</identifier><identifier>DOI: 10.1007/s10473-023-0306-1</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Analysis ; Mathematics ; Mathematics and Statistics</subject><ispartof>Acta mathematica scientia, 2023-05, Vol.43 (3), p.1081-1104</ispartof><rights>Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2023</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c274t-6a731d5c447f52e553ee46064dee547f6e5a216976cdebf6b4ee8023b64e35713</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.wanfangdata.com.cn/images/PeriodicalImages/sxwlxb-e/sxwlxb-e.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10473-023-0306-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10473-023-0306-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Pu, Xueke</creatorcontrib><creatorcontrib>Zhou, Wenli</creatorcontrib><title>On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification</title><title>Acta mathematica scientia</title><addtitle>Acta Math Sci</addtitle><description>In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.</description><subject>Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0252-9602</issn><issn>1572-9087</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kElPwzAQhS0EEqXwA7j5yiFgO17aIyplkYqK2K6Wk05SV20Cdrr9eyYNEicOlsfj773RPEIuObvmjJmbyJk0acIEnpTphB-RHldGJEM2MMekx4TCWjNxSs5iXDDGtdCyR8ppRZs50Fdf1qFeR_rs8Llyjc_dkt5B8Bus64oWdTiAnz7mLfcS_Mo3fgN0_L0-IJFufTNHTRV9s6dvTcB2gT7t5zk5KdwywsXv3Scf9-P30WMymT48jW4nSS6MbBLtTMpnKpfSFEqAUimA1EzLGYDCngblBNdDo_MZZIXOJMAAl860hFQZnvbJVee7dVXhqtIu6nWocKKNu-1yl1kQiGNETCPLOzYPdYwBCvuFS7mwt5zZNlXbpWpRYdtUbesvOk1Etioh_A34X_QD53J7rQ</recordid><startdate>20230501</startdate><enddate>20230501</enddate><creator>Pu, Xueke</creator><creator>Zhou, Wenli</creator><general>Springer Nature Singapore</general><general>School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China</general><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20230501</creationdate><title>On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification</title><author>Pu, Xueke ; Zhou, Wenli</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c274t-6a731d5c447f52e553ee46064dee547f6e5a216976cdebf6b4ee8023b64e35713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pu, Xueke</creatorcontrib><creatorcontrib>Zhou, Wenli</creatorcontrib><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Acta mathematica scientia</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pu, Xueke</au><au>Zhou, Wenli</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification</atitle><jtitle>Acta mathematica scientia</jtitle><stitle>Acta Math Sci</stitle><date>2023-05-01</date><risdate>2023</risdate><volume>43</volume><issue>3</issue><spage>1081</spage><epage>1104</epage><pages>1081-1104</pages><issn>0252-9602</issn><eissn>1572-9087</eissn><abstract>In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s10473-023-0306-1</doi><tpages>24</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0252-9602
ispartof Acta mathematica scientia, 2023-05, Vol.43 (3), p.1081-1104
issn 0252-9602
1572-9087
language eng
recordid cdi_wanfang_journals_sxwlxb_e202303006
source SpringerNature Journals; Alma/SFX Local Collection
subjects Analysis
Mathematics
Mathematics and Statistics
title On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-22T14%3A04%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wanfang_jour_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Rigorous%20Mathematical%20Derivation%20for%20the%20Viscous%20Primitive%20Equations%20with%20Density%20Stratification&rft.jtitle=Acta%20mathematica%20scientia&rft.au=Pu,%20Xueke&rft.date=2023-05-01&rft.volume=43&rft.issue=3&rft.spage=1081&rft.epage=1104&rft.pages=1081-1104&rft.issn=0252-9602&rft.eissn=1572-9087&rft_id=info:doi/10.1007/s10473-023-0306-1&rft_dat=%3Cwanfang_jour_cross%3Esxwlxb_e202303006%3C/wanfang_jour_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_wanfj_id=sxwlxb_e202303006&rfr_iscdi=true