Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type
This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the H 4 × H 3 framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in L 2 -nor...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2020-08, Vol.71 (4), Article 108 |
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| creator | Gao, Jincheng Lyu, Zeyu Yao, Zheng-an |
| description | This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the
H
4
×
H
3
framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in
L
2
-norm is
(
1
+
t
)
-
3
4
if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the
k
(
k
∈
[
1
,
3
]
)
th-order spatial derivatives of solution converging to zero in
L
2
-norm is
(
1
+
t
)
-
3
+
2
k
4
. Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in
L
2
-norm is
(
1
+
t
)
-
5
4
. |
| doi_str_mv | 10.1007/s00033-020-01330-8 |
| format | Article |
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H
4
×
H
3
framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in
L
2
-norm is
(
1
+
t
)
-
3
4
if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the
k
(
k
∈
[
1
,
3
]
)
th-order spatial derivatives of solution converging to zero in
L
2
-norm is
(
1
+
t
)
-
3
+
2
k
4
. Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in
L
2
-norm is
(
1
+
t
)
-
5
4
.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-020-01330-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Compressible fluids ; Computational fluid dynamics ; Convergence ; Decay rate ; Derivatives ; Engineering ; Lower bounds ; Mathematical Methods in Physics ; Matter & antimatter ; Theoretical and Applied Mechanics</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2020-08, Vol.71 (4), Article 108</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-347578275ac874c49437294cf9c764cf46ac24b19f867bf975419e51cf90db2a3</citedby><cites>FETCH-LOGICAL-c319t-347578275ac874c49437294cf9c764cf46ac24b19f867bf975419e51cf90db2a3</cites><orcidid>0000-0002-2914-8952</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00033-020-01330-8$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-020-01330-8$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gao, Jincheng</creatorcontrib><creatorcontrib>Lyu, Zeyu</creatorcontrib><creatorcontrib>Yao, Zheng-an</creatorcontrib><title>Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the
H
4
×
H
3
framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in
L
2
-norm is
(
1
+
t
)
-
3
4
if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the
k
(
k
∈
[
1
,
3
]
)
th-order spatial derivatives of solution converging to zero in
L
2
-norm is
(
1
+
t
)
-
3
+
2
k
4
. Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in
L
2
-norm is
(
1
+
t
)
-
5
4
.</description><subject>Compressible fluids</subject><subject>Computational fluid dynamics</subject><subject>Convergence</subject><subject>Decay rate</subject><subject>Derivatives</subject><subject>Engineering</subject><subject>Lower bounds</subject><subject>Mathematical Methods in Physics</subject><subject>Matter & antimatter</subject><subject>Theoretical and Applied Mechanics</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kEtPwzAQhC0EEqXwBzhZ4mzwK3F8RBUvUYkLnK3E2bSp0jjYTqv-e9wGiRuH1Wilb2ZXg9Ato_eMUvUQKKVCEMopoUwISoozNGMyrZoKfY5mlEpJOFfZJboKYZNwxaiYobh0e_C4cmNfY9fgGmx5wL6MgBvn8bpdrcET5-sEpWl3ZWx3EI5ocN0YW9fj6HBcA7ZuO3gIoa26ZO7GtsZbV0N3gt-dj7CHFY6HAa7RRVN2AW5-dY6-np8-F69k-fHytnhcEiuYjkRIlaki_VzaQkkrtRSKa2kbbVWeROal5bJiuilyVTVaZZJpyFgCaF3xUszR3ZQ7ePc9Qohm40bfp5OGS8azLOciTxSfKOtdCB4aM_h2W_qDYdQc2zVTuya1a07tmiKZxGQKCe5X4P-i_3H9AF2ufYw</recordid><startdate>20200801</startdate><enddate>20200801</enddate><creator>Gao, Jincheng</creator><creator>Lyu, Zeyu</creator><creator>Yao, Zheng-an</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2914-8952</orcidid></search><sort><creationdate>20200801</creationdate><title>Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type</title><author>Gao, Jincheng ; Lyu, Zeyu ; Yao, Zheng-an</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-347578275ac874c49437294cf9c764cf46ac24b19f867bf975419e51cf90db2a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Compressible fluids</topic><topic>Computational fluid dynamics</topic><topic>Convergence</topic><topic>Decay rate</topic><topic>Derivatives</topic><topic>Engineering</topic><topic>Lower bounds</topic><topic>Mathematical Methods in Physics</topic><topic>Matter & antimatter</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gao, Jincheng</creatorcontrib><creatorcontrib>Lyu, Zeyu</creatorcontrib><creatorcontrib>Yao, Zheng-an</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gao, Jincheng</au><au>Lyu, Zeyu</au><au>Yao, Zheng-an</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2020-08-01</date><risdate>2020</risdate><volume>71</volume><issue>4</issue><artnum>108</artnum><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the
H
4
×
H
3
framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in
L
2
-norm is
(
1
+
t
)
-
3
4
if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the
k
(
k
∈
[
1
,
3
]
)
th-order spatial derivatives of solution converging to zero in
L
2
-norm is
(
1
+
t
)
-
3
+
2
k
4
. Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in
L
2
-norm is
(
1
+
t
)
-
5
4
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-020-01330-8</doi><orcidid>https://orcid.org/0000-0002-2914-8952</orcidid><oa>free_for_read</oa></addata></record> |
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| issn | 0044-2275 1420-9039 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Compressible fluids Computational fluid dynamics Convergence Decay rate Derivatives Engineering Lower bounds Mathematical Methods in Physics Matter & antimatter Theoretical and Applied Mechanics |
| title | Lower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type |
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