On the Temporal Decay for the 2D Non-resistive Incompressible MHD Equations
Califano–Chiuderi (Phys Rev E 60(Part B): 4701–4707, 1999) gave the numerical observation that the energy of the MHD equations is dissipated at a rate independent of the ohmic resistivity, which was first proved by Ren et al. (J Funct Anal 267: 503–541, 2014) (the initial data near ( 0 , e → 1 ) , e...
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| Veröffentlicht in: | Annales Henri Poincaré 2023-06, Vol.24 (6), p.2005-2065 |
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| creator | Wan, Renhui |
| description | Califano–Chiuderi (Phys Rev E 60(Part B): 4701–4707, 1999) gave the numerical observation that the energy of the MHD equations is dissipated at a rate independent of the ohmic resistivity, which was first proved by Ren et al. (J Funct Anal 267: 503–541, 2014) (the initial data near
(
0
,
e
→
1
)
,
e
→
1
=
(
1
,
0
)
). Precisely, they showed some explicit decay rates of solutions in
L
2
norm. So a nature question is whether the obtained decay rates in Ren et al. (J Funct Anal 267: 503–541, 2014) are optimal. In this paper, we aim at giving the explicit decay rates of solutions in both
L
2
norm and
L
∞
norm. In particular, our decay rate in terms of
L
2
norm improves the previous work Ren et al. (J Funct Anal 267: 503–541, 2014). |
| doi_str_mv | 10.1007/s00023-023-01268-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2812063092</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2812063092</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-8bd762836fdb29f6aa9ba9297995edf91a3765696f5ad9d256de4f25e8c0d3303</originalsourceid><addsrcrecordid>eNp9UMtOAjEUbYwmIvoDrpq4rt62TGe6NIBCRNnguulMWx0C06EdTPh7C2N05-LmPnIeuQehWwr3FCB_iADAODkVZaIg_AwN6IiNCAhBz39nnl-iqxjXkFAFlwP0smxw92nxym5bH_QGT2ylD9j5cDqzCX7zDQk21rGrvyyeN5XftmmPdbmx-HU2wdPdXne1b-I1unB6E-3NTx-i96fpajwji-XzfPy4IBXLoSNFaXKR3IUzJZNOaC1LLZnMpcyscZJqnotMSOEybaRhmTB25FhmiwoM58CH6K7XbYPf7W3s1NrvQ5MsFSsoS1-CZAnFelQVfIzBOtWGeqvDQVFQx9BUH5o61TE0xROJ96SYwM2HDX_S_7C-AfadbcM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2812063092</pqid></control><display><type>article</type><title>On the Temporal Decay for the 2D Non-resistive Incompressible MHD Equations</title><source>SpringerLink Journals - AutoHoldings</source><creator>Wan, Renhui</creator><creatorcontrib>Wan, Renhui</creatorcontrib><description>Califano–Chiuderi (Phys Rev E 60(Part B): 4701–4707, 1999) gave the numerical observation that the energy of the MHD equations is dissipated at a rate independent of the ohmic resistivity, which was first proved by Ren et al. (J Funct Anal 267: 503–541, 2014) (the initial data near
(
0
,
e
→
1
)
,
e
→
1
=
(
1
,
0
)
). Precisely, they showed some explicit decay rates of solutions in
L
2
norm. So a nature question is whether the obtained decay rates in Ren et al. (J Funct Anal 267: 503–541, 2014) are optimal. In this paper, we aim at giving the explicit decay rates of solutions in both
L
2
norm and
L
∞
norm. In particular, our decay rate in terms of
L
2
norm improves the previous work Ren et al. (J Funct Anal 267: 503–541, 2014).</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-023-01268-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Classical and Quantum Gravitation ; Decay rate ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Original Paper ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Annales Henri Poincaré, 2023-06, Vol.24 (6), p.2005-2065</ispartof><rights>Springer Nature Switzerland AG 2023. 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><cites>FETCH-LOGICAL-c270t-8bd762836fdb29f6aa9ba9297995edf91a3765696f5ad9d256de4f25e8c0d3303</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/s00023-023-01268-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00023-023-01268-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Wan, Renhui</creatorcontrib><title>On the Temporal Decay for the 2D Non-resistive Incompressible MHD Equations</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>Califano–Chiuderi (Phys Rev E 60(Part B): 4701–4707, 1999) gave the numerical observation that the energy of the MHD equations is dissipated at a rate independent of the ohmic resistivity, which was first proved by Ren et al. (J Funct Anal 267: 503–541, 2014) (the initial data near
(
0
,
e
→
1
)
,
e
→
1
=
(
1
,
0
)
). Precisely, they showed some explicit decay rates of solutions in
L
2
norm. So a nature question is whether the obtained decay rates in Ren et al. (J Funct Anal 267: 503–541, 2014) are optimal. In this paper, we aim at giving the explicit decay rates of solutions in both
L
2
norm and
L
∞
norm. In particular, our decay rate in terms of
L
2
norm improves the previous work Ren et al. (J Funct Anal 267: 503–541, 2014).</description><subject>Classical and Quantum Gravitation</subject><subject>Decay rate</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Original Paper</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UMtOAjEUbYwmIvoDrpq4rt62TGe6NIBCRNnguulMWx0C06EdTPh7C2N05-LmPnIeuQehWwr3FCB_iADAODkVZaIg_AwN6IiNCAhBz39nnl-iqxjXkFAFlwP0smxw92nxym5bH_QGT2ylD9j5cDqzCX7zDQk21rGrvyyeN5XftmmPdbmx-HU2wdPdXne1b-I1unB6E-3NTx-i96fpajwji-XzfPy4IBXLoSNFaXKR3IUzJZNOaC1LLZnMpcyscZJqnotMSOEybaRhmTB25FhmiwoM58CH6K7XbYPf7W3s1NrvQ5MsFSsoS1-CZAnFelQVfIzBOtWGeqvDQVFQx9BUH5o61TE0xROJ96SYwM2HDX_S_7C-AfadbcM</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Wan, Renhui</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230601</creationdate><title>On the Temporal Decay for the 2D Non-resistive Incompressible MHD Equations</title><author>Wan, Renhui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-8bd762836fdb29f6aa9ba9297995edf91a3765696f5ad9d256de4f25e8c0d3303</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Decay rate</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Original Paper</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wan, Renhui</creatorcontrib><collection>CrossRef</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wan, Renhui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Temporal Decay for the 2D Non-resistive Incompressible MHD Equations</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>24</volume><issue>6</issue><spage>2005</spage><epage>2065</epage><pages>2005-2065</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>Califano–Chiuderi (Phys Rev E 60(Part B): 4701–4707, 1999) gave the numerical observation that the energy of the MHD equations is dissipated at a rate independent of the ohmic resistivity, which was first proved by Ren et al. (J Funct Anal 267: 503–541, 2014) (the initial data near
(
0
,
e
→
1
)
,
e
→
1
=
(
1
,
0
)
). Precisely, they showed some explicit decay rates of solutions in
L
2
norm. So a nature question is whether the obtained decay rates in Ren et al. (J Funct Anal 267: 503–541, 2014) are optimal. In this paper, we aim at giving the explicit decay rates of solutions in both
L
2
norm and
L
∞
norm. In particular, our decay rate in terms of
L
2
norm improves the previous work Ren et al. (J Funct Anal 267: 503–541, 2014).</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00023-023-01268-3</doi><tpages>61</tpages></addata></record> |
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| subjects | Classical and Quantum Gravitation Decay rate Dynamical Systems and Ergodic Theory Elementary Particles Mathematical and Computational Physics Mathematical Methods in Physics Original Paper Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Theoretical |
| title | On the Temporal Decay for the 2D Non-resistive Incompressible MHD Equations |
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