Stability of degree-2 Rossby-Haurwitz waves
Rossby-Haurwitz (RH) waves are important explicit solutions of the incompressible Euler equation on a two-dimensional rotating sphere. In this paper, we prove the orbital stability of degree-2 RH waves, which confirms a conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech. Anal...
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| creator | Cao, Daomin Wang, Guodong Zuo, Bijun |
| description | Rossby-Haurwitz (RH) waves are important explicit solutions of the
incompressible Euler equation on a two-dimensional rotating sphere. In this
paper, we prove the orbital stability of degree-2 RH waves, which confirms a
conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech.
Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with
the main challenge being to establish suitable variational characterizations
for the solutions under consideration. In this process, the set of
rearrangements of a fixed function plays a vital role. We also apply our
approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and
zonal flows with monotone absolute vorticity. |
| doi_str_mv | 10.48550/arxiv.2305.03279 |
| format | Article |
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incompressible Euler equation on a two-dimensional rotating sphere. In this
paper, we prove the orbital stability of degree-2 RH waves, which confirms a
conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech.
Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with
the main challenge being to establish suitable variational characterizations
for the solutions under consideration. In this process, the set of
rearrangements of a fixed function plays a vital role. We also apply our
approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and
zonal flows with monotone absolute vorticity.</description><identifier>DOI: 10.48550/arxiv.2305.03279</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2023-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2305.03279$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2305.03279$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Cao, Daomin</creatorcontrib><creatorcontrib>Wang, Guodong</creatorcontrib><creatorcontrib>Zuo, Bijun</creatorcontrib><title>Stability of degree-2 Rossby-Haurwitz waves</title><description>Rossby-Haurwitz (RH) waves are important explicit solutions of the
incompressible Euler equation on a two-dimensional rotating sphere. In this
paper, we prove the orbital stability of degree-2 RH waves, which confirms a
conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech.
Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with
the main challenge being to establish suitable variational characterizations
for the solutions under consideration. In this process, the set of
rearrangements of a fixed function plays a vital role. We also apply our
approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and
zonal flows with monotone absolute vorticity.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzs1qAjEUQOFsXBT1Abrq7EvGm2SSO1kWqVUQBOt-uJkkJaAomal2fPriz-rsDh9jrwLKqtYaZpT_0rmUCnQJSqJ9Ye_fPbm0T_1QHGPhw08Ogctie-w6N_Al_eZL6q_Fhc6hm7BRpH0Xps-O2W7xuZsv-XrztZp_rDkZtFw4BKAWa2mRZGhBK63IhapFdF4IqExwKF0U1npTR2kr8IaMcq3XMqIas7fH9q5tTjkdKA_NTd3c1eofiJo7tw</recordid><startdate>20230505</startdate><enddate>20230505</enddate><creator>Cao, Daomin</creator><creator>Wang, Guodong</creator><creator>Zuo, Bijun</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230505</creationdate><title>Stability of degree-2 Rossby-Haurwitz waves</title><author>Cao, Daomin ; Wang, Guodong ; Zuo, Bijun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-1b700ac78297a2ec05353abe4c77bd11046eb72bf199d68f2940d6a63bcd52f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Cao, Daomin</creatorcontrib><creatorcontrib>Wang, Guodong</creatorcontrib><creatorcontrib>Zuo, Bijun</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Cao, Daomin</au><au>Wang, Guodong</au><au>Zuo, Bijun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability of degree-2 Rossby-Haurwitz waves</atitle><date>2023-05-05</date><risdate>2023</risdate><abstract>Rossby-Haurwitz (RH) waves are important explicit solutions of the
incompressible Euler equation on a two-dimensional rotating sphere. In this
paper, we prove the orbital stability of degree-2 RH waves, which confirms a
conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech.
Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with
the main challenge being to establish suitable variational characterizations
for the solutions under consideration. In this process, the set of
rearrangements of a fixed function plays a vital role. We also apply our
approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and
zonal flows with monotone absolute vorticity.</abstract><doi>10.48550/arxiv.2305.03279</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Stability of degree-2 Rossby-Haurwitz waves |
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