Flexibility and Rigidity in Steady Fluid Motion
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dim...
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| Veröffentlicht in: | Communications in mathematical physics 2021-07, Vol.385 (1), p.521-563 |
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| container_title | Communications in mathematical physics |
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| creator | Constantin, Peter Drivas, Theodore D. Ginsberg, Daniel |
| description | Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol’d stable solutions are shown to be structurally stable. |
| doi_str_mv | 10.1007/s00220-021-04048-4 |
| format | Article |
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Math. Phys</addtitle><description>Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol’d stable solutions are shown to be structurally stable.</description><subject>Boussinesq equations</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Domains</subject><subject>Flexibility</subject><subject>Magnetic properties</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Perturbation</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Rigidity</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKw0AUhgdRsFZfwFXA9dgzl0wySynWChXBy3qYa5kSkzqTgH17UyO4c3U4nO__D3wIXRO4JQDVIgNQChgowcCB15ifoBnhjGKQRJyiGQABzAQR5-gi5x0ASCrEDC1Wjf-KJjaxPxS6dcVL3EZ3XGJbvPZeu0Oxaoboiqeuj117ic6CbrK_-p1z9L66f1uu8eb54XF5t8GW1WWPpbbWV5KD0SxYqkMJQZSOOiZFFSww7QyriNEWgpZGC02Cq01Nx5shoNkc3Uy9-9R9Dj73atcNqR1fKlpyVnHCazlSdKJs6nJOPqh9ih86HRQBdRSjJjFqFKN-xCg-htgUyiPcbn36q_4n9Q3n5GWH</recordid><startdate>20210701</startdate><enddate>20210701</enddate><creator>Constantin, Peter</creator><creator>Drivas, Theodore D.</creator><creator>Ginsberg, Daniel</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-2818-0376</orcidid></search><sort><creationdate>20210701</creationdate><title>Flexibility and Rigidity in Steady Fluid Motion</title><author>Constantin, Peter ; Drivas, Theodore D. ; Ginsberg, Daniel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c385t-9acce7940ba3fc2af50f65d2d3967fc03adb371bac0fa9ba6a1fd8b82fc0b10a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Boussinesq equations</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Domains</topic><topic>Flexibility</topic><topic>Magnetic properties</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Perturbation</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Rigidity</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Constantin, Peter</creatorcontrib><creatorcontrib>Drivas, Theodore D.</creatorcontrib><creatorcontrib>Ginsberg, Daniel</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Constantin, Peter</au><au>Drivas, Theodore D.</au><au>Ginsberg, Daniel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Flexibility and Rigidity in Steady Fluid Motion</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. 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| ispartof | Communications in mathematical physics, 2021-07, Vol.385 (1), p.521-563 |
| issn | 0010-3616 1432-0916 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Boussinesq equations Classical and Quantum Gravitation Complex Systems Domains Flexibility Magnetic properties Mathematical and Computational Physics Mathematical Physics Perturbation Physics Physics and Astronomy Quantum Physics Relativity Theory Rigidity Theoretical |
| title | Flexibility and Rigidity in Steady Fluid Motion |
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