Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit
In this short note, we prove that given initial data u 0 ∈ H s ( R ) with s > 3 2 and for some T > 0 , the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in L ∞ ( 0 , T ; H s ( R ) ) to the inviscid Burgers equation as the filter parameter α...
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| Veröffentlicht in: | Monatshefte für Mathematik 2024, Vol.205 (1), p.177-185 |
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| container_title | Monatshefte für Mathematik |
| container_volume | 205 |
| creator | Li, Jinlu Yu, Yanghai Zhu, Weipeng |
| description | In this short note, we prove that given initial data
u
0
∈
H
s
(
R
)
with
s
>
3
2
and for some
T
>
0
, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in
L
∞
(
0
,
T
;
H
s
(
R
)
)
to the inviscid Burgers equation as the filter parameter
α
tends to zero. This is a complement of our recent result on the zero-filter limit. |
| doi_str_mv | 10.1007/s00605-023-01931-1 |
| format | Article |
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u
0
∈
H
s
(
R
)
with
s
>
3
2
and for some
T
>
0
, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in
L
∞
(
0
,
T
;
H
s
(
R
)
)
to the inviscid Burgers equation as the filter parameter
α
tends to zero. This is a complement of our recent result on the zero-filter limit.</description><identifier>ISSN: 0026-9255</identifier><identifier>EISSN: 1436-5081</identifier><identifier>DOI: 10.1007/s00605-023-01931-1</identifier><language>eng</language><publisher>Vienna: Springer Vienna</publisher><subject>Burgers equation ; Fluid dynamics ; Mathematics ; Mathematics and Statistics ; Partial differential equations</subject><ispartof>Monatshefte für Mathematik, 2024, Vol.205 (1), p.177-185</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-11501e38359fce66f749084ec2ba81860c16c8b401bd05990b0be4788b1b184c3</citedby><cites>FETCH-LOGICAL-c319t-11501e38359fce66f749084ec2ba81860c16c8b401bd05990b0be4788b1b184c3</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/s00605-023-01931-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00605-023-01931-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Li, Jinlu</creatorcontrib><creatorcontrib>Yu, Yanghai</creatorcontrib><creatorcontrib>Zhu, Weipeng</creatorcontrib><title>Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit</title><title>Monatshefte für Mathematik</title><addtitle>Monatsh Math</addtitle><description>In this short note, we prove that given initial data
u
0
∈
H
s
(
R
)
with
s
>
3
2
and for some
T
>
0
, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in
L
∞
(
0
,
T
;
H
s
(
R
)
)
to the inviscid Burgers equation as the filter parameter
α
tends to zero. This is a complement of our recent result on the zero-filter limit.</description><subject>Burgers equation</subject><subject>Fluid dynamics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial differential equations</subject><issn>0026-9255</issn><issn>1436-5081</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKxDAURYMoOI7-gKuA6-h7TZMmSxnUEQbd6E4IbUzHDm0yk7SCrvwH_9Avsc4I7ly9xb3nPjiEnCKcI0BxkQAkCAYZZ4CaI8M9MsGcSyZA4T6ZAGSS6UyIQ3KU0goAkEs9IU93wbPBN3WIHbXBv7q4dN46GmqaQjv0TfB0DGn_4uis7MqUyq-Pz3loO-o2Q7nNG7-N310MrG7a3kXaNl3TH5ODumyTO_m9U_J4ffUwm7PF_c3t7HLBLEfdM0QB6LjiQtfWSVkXuQaVO5tVpUIlwaK0qsoBq2cQWkMFlcsLpSqsUOWWT8nZbncdw2ZwqTerMEQ_vjQctEQpCqHGVrZr2RhSiq4269h0ZXwzCObHotlZNKNFs7VocIT4Dkpj2S9d_Jv-h_oG_ux1fA</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Li, Jinlu</creator><creator>Yu, Yanghai</creator><creator>Zhu, Weipeng</creator><general>Springer Vienna</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2024</creationdate><title>Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit</title><author>Li, Jinlu ; Yu, Yanghai ; Zhu, Weipeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-11501e38359fce66f749084ec2ba81860c16c8b401bd05990b0be4788b1b184c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Burgers equation</topic><topic>Fluid dynamics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Jinlu</creatorcontrib><creatorcontrib>Yu, Yanghai</creatorcontrib><creatorcontrib>Zhu, Weipeng</creatorcontrib><collection>CrossRef</collection><jtitle>Monatshefte für Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Jinlu</au><au>Yu, Yanghai</au><au>Zhu, Weipeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit</atitle><jtitle>Monatshefte für Mathematik</jtitle><stitle>Monatsh Math</stitle><date>2024</date><risdate>2024</risdate><volume>205</volume><issue>1</issue><spage>177</spage><epage>185</epage><pages>177-185</pages><issn>0026-9255</issn><eissn>1436-5081</eissn><abstract>In this short note, we prove that given initial data
u
0
∈
H
s
(
R
)
with
s
>
3
2
and for some
T
>
0
, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in
L
∞
(
0
,
T
;
H
s
(
R
)
)
to the inviscid Burgers equation as the filter parameter
α
tends to zero. This is a complement of our recent result on the zero-filter limit.</abstract><cop>Vienna</cop><pub>Springer Vienna</pub><doi>10.1007/s00605-023-01931-1</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0026-9255 |
| ispartof | Monatshefte für Mathematik, 2024, Vol.205 (1), p.177-185 |
| issn | 0026-9255 1436-5081 |
| language | eng |
| recordid | cdi_proquest_journals_3096165758 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Burgers equation Fluid dynamics Mathematics Mathematics and Statistics Partial differential equations |
| title | Non-uniform convergence of solution for the Camassa–Holm equation in the zero-filter limit |
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