A regularity result for incompressible elastodynamics equations in the ALE coordinates
We consider incompressible inviscid elastodynamics equations with a free surface and establish regularity of solutions for these equations. Compared with previous result on this free boundary problem [X. Gu and F. Wang, Well-posedness of the free boundary problem in incompressible elastodynamic unde...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-01-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2023-0156 |
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| author | Xie Binqiang |
| author_facet | Xie Binqiang |
| author_sort | Xie Binqiang |
| collection | DOAJ |
| description | We consider incompressible inviscid elastodynamics equations with a free surface and establish regularity of solutions for these equations. Compared with previous result on this free boundary problem [X. Gu and F. Wang, Well-posedness of the free boundary problem in incompressible elastodynamic under the mixed type stability condition, J. Math. Anal. Appl., 482, (2020), 123529] in space H
3, we are able to establish regularity in space H
2.5+δ
upon the Arbitrary Lagrangian-Eulerian (ALE) coordinates. It is achieved by reformulating the system into a new formulation with the ALE coordinates, presenting uniform estimates for the pressure, tangential estimates for the system, as well as curl and divergence estimates. |
| format | Article |
| id | doaj-art-2f7afbf77bc84ed1b2bd523a6e8b9fb8 |
| institution | OA Journals |
| issn | 2169-0375 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj-art-2f7afbf77bc84ed1b2bd523a6e8b9fb82025-08-20T02:00:52ZengDe GruyterAdvanced Nonlinear Studies2169-03752025-01-0125120422410.1515/ans-2023-0156A regularity result for incompressible elastodynamics equations in the ALE coordinatesXie Binqiang0School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, Guangdong, 510006, ChinaWe consider incompressible inviscid elastodynamics equations with a free surface and establish regularity of solutions for these equations. Compared with previous result on this free boundary problem [X. Gu and F. Wang, Well-posedness of the free boundary problem in incompressible elastodynamic under the mixed type stability condition, J. Math. Anal. Appl., 482, (2020), 123529] in space H 3, we are able to establish regularity in space H 2.5+δ upon the Arbitrary Lagrangian-Eulerian (ALE) coordinates. It is achieved by reformulating the system into a new formulation with the ALE coordinates, presenting uniform estimates for the pressure, tangential estimates for the system, as well as curl and divergence estimates.https://doi.org/10.1515/ans-2023-0156free boundaryincompressible elastodynamics equationsa priori estimates76n1035q3535d3576e19 |
| spellingShingle | Xie Binqiang A regularity result for incompressible elastodynamics equations in the ALE coordinates Advanced Nonlinear Studies free boundary incompressible elastodynamics equations a priori estimates 76n10 35q35 35d35 76e19 |
| title | A regularity result for incompressible elastodynamics equations in the ALE coordinates |
| title_full | A regularity result for incompressible elastodynamics equations in the ALE coordinates |
| title_fullStr | A regularity result for incompressible elastodynamics equations in the ALE coordinates |
| title_full_unstemmed | A regularity result for incompressible elastodynamics equations in the ALE coordinates |
| title_short | A regularity result for incompressible elastodynamics equations in the ALE coordinates |
| title_sort | regularity result for incompressible elastodynamics equations in the ale coordinates |
| topic | free boundary incompressible elastodynamics equations a priori estimates 76n10 35q35 35d35 76e19 |
| url | https://doi.org/10.1515/ans-2023-0156 |
| work_keys_str_mv | AT xiebinqiang aregularityresultforincompressibleelastodynamicsequationsinthealecoordinates AT xiebinqiang regularityresultforincompressibleelastodynamicsequationsinthealecoordinates |