Transition Threshold for the 2-D Couette Flow in a Finite Channel
In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations around the Couette flow ( y , 0) at high Reynolds number Re in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the...
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2020-10, Vol.238 (1), p.125-183 |
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| creator | Chen, Qi Li, Te Wei, Dongyi Zhang, Zhifei |
| description | In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations around the Couette flow (
y
, 0) at high Reynolds number
Re
in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier–Stokes equations. In particular, three kinds of important effects—enhanced dissipation, inviscid damping and a boundary layer–are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity
v
0
satisfies
‖
v
0
-
(
y
,
0
)
‖
H
2
≦
c
R
e
-
1
2
for some small
c
independent of
Re
, then the solution of the 2-D Navier–Stokes equations remains within
O
(
R
e
-
1
2
)
of the Couette flow for any time. |
| doi_str_mv | 10.1007/s00205-020-01538-y |
| format | Article |
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y
, 0) at high Reynolds number
Re
in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier–Stokes equations. In particular, three kinds of important effects—enhanced dissipation, inviscid damping and a boundary layer–are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity
v
0
satisfies
‖
v
0
-
(
y
,
0
)
‖
H
2
≦
c
R
e
-
1
2
for some small
c
independent of
Re
, then the solution of the 2-D Navier–Stokes equations remains within
O
(
R
e
-
1
2
)
of the Couette flow for any time.</description><identifier>ISSN: 0003-9527</identifier><identifier>EISSN: 1432-0673</identifier><identifier>DOI: 10.1007/s00205-020-01538-y</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Boundary layers ; Classical Mechanics ; Complex Systems ; Couette flow ; Damping ; Estimates ; Fluid dynamics ; Fluid flow ; Fluid- and Aerodynamics ; High Reynolds number ; Linearization ; Mathematical analysis ; Mathematical and Computational Physics ; Navier-Stokes equations ; Physics ; Physics and Astronomy ; Reynolds number ; Spacetime ; Theoretical ; Two dimensional flow</subject><ispartof>Archive for rational mechanics and analysis, 2020-10, Vol.238 (1), p.125-183</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-af4ca3f86fb311e0fbbb627524ab86d729d5cfa49f19364ed9315502b63c47de3</citedby><cites>FETCH-LOGICAL-c319t-af4ca3f86fb311e0fbbb627524ab86d729d5cfa49f19364ed9315502b63c47de3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00205-020-01538-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00205-020-01538-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Chen, Qi</creatorcontrib><creatorcontrib>Li, Te</creatorcontrib><creatorcontrib>Wei, Dongyi</creatorcontrib><creatorcontrib>Zhang, Zhifei</creatorcontrib><title>Transition Threshold for the 2-D Couette Flow in a Finite Channel</title><title>Archive for rational mechanics and analysis</title><addtitle>Arch Rational Mech Anal</addtitle><description>In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations around the Couette flow (
y
, 0) at high Reynolds number
Re
in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier–Stokes equations. In particular, three kinds of important effects—enhanced dissipation, inviscid damping and a boundary layer–are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity
v
0
satisfies
‖
v
0
-
(
y
,
0
)
‖
H
2
≦
c
R
e
-
1
2
for some small
c
independent of
Re
, then the solution of the 2-D Navier–Stokes equations remains within
O
(
R
e
-
1
2
)
of the Couette flow for any time.</description><subject>Boundary layers</subject><subject>Classical Mechanics</subject><subject>Complex Systems</subject><subject>Couette flow</subject><subject>Damping</subject><subject>Estimates</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Fluid- and Aerodynamics</subject><subject>High Reynolds number</subject><subject>Linearization</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Navier-Stokes equations</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Reynolds number</subject><subject>Spacetime</subject><subject>Theoretical</subject><subject>Two dimensional flow</subject><issn>0003-9527</issn><issn>1432-0673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</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>eNp9kE9LxDAQxYMouK5-AU8Bz9HJ37bHpboqLHhZzyFtE9ulJmvSRfbbG63gzcsbZnjvDfwQuqZwSwGKuwTAQJIsBKjkJTmeoAUVnBFQBT9FCwDgpJKsOEcXKe2-V8bVAq220fg0TEPweNtHm_owdtiFiKfeYkbucR0OdposXo_hEw8eG7we_JAPdW-8t-MlOnNmTPbqdy7R6_phWz-Rzcvjc73akJbTaiLGidZwVyrXcEotuKZpFCskE6YpVVewqpOtM6JytOJK2K7iVEpgjeKtKDrLl-hm7t3H8HGwadK7cIg-v9RMMMokSCizi82uNoaUonV6H4d3E4-agv5GpWdUOov-QaWPOcTnUMpm_2bjX_U_qS9WwGrK</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>Chen, Qi</creator><creator>Li, Te</creator><creator>Wei, Dongyi</creator><creator>Zhang, Zhifei</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><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>20201001</creationdate><title>Transition Threshold for the 2-D Couette Flow in a Finite Channel</title><author>Chen, Qi ; Li, Te ; Wei, Dongyi ; Zhang, Zhifei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-af4ca3f86fb311e0fbbb627524ab86d729d5cfa49f19364ed9315502b63c47de3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Boundary layers</topic><topic>Classical Mechanics</topic><topic>Complex Systems</topic><topic>Couette flow</topic><topic>Damping</topic><topic>Estimates</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Fluid- and Aerodynamics</topic><topic>High Reynolds number</topic><topic>Linearization</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Navier-Stokes equations</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Reynolds number</topic><topic>Spacetime</topic><topic>Theoretical</topic><topic>Two dimensional flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Qi</creatorcontrib><creatorcontrib>Li, Te</creatorcontrib><creatorcontrib>Wei, Dongyi</creatorcontrib><creatorcontrib>Zhang, Zhifei</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Archive for rational mechanics and analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Qi</au><au>Li, Te</au><au>Wei, Dongyi</au><au>Zhang, Zhifei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Transition Threshold for the 2-D Couette Flow in a Finite Channel</atitle><jtitle>Archive for rational mechanics and analysis</jtitle><stitle>Arch Rational Mech Anal</stitle><date>2020-10-01</date><risdate>2020</risdate><volume>238</volume><issue>1</issue><spage>125</spage><epage>183</epage><pages>125-183</pages><issn>0003-9527</issn><eissn>1432-0673</eissn><abstract>In this paper, we study the transition threshold problem for the 2-D Navier–Stokes equations around the Couette flow (
y
, 0) at high Reynolds number
Re
in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier–Stokes equations. In particular, three kinds of important effects—enhanced dissipation, inviscid damping and a boundary layer–are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity
v
0
satisfies
‖
v
0
-
(
y
,
0
)
‖
H
2
≦
c
R
e
-
1
2
for some small
c
independent of
Re
, then the solution of the 2-D Navier–Stokes equations remains within
O
(
R
e
-
1
2
)
of the Couette flow for any time.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00205-020-01538-y</doi><tpages>59</tpages></addata></record> |
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| language | eng |
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| subjects | Boundary layers Classical Mechanics Complex Systems Couette flow Damping Estimates Fluid dynamics Fluid flow Fluid- and Aerodynamics High Reynolds number Linearization Mathematical analysis Mathematical and Computational Physics Navier-Stokes equations Physics Physics and Astronomy Reynolds number Spacetime Theoretical Two dimensional flow |
| title | Transition Threshold for the 2-D Couette Flow in a Finite Channel |
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