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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-01-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2023-0156 |
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| Summary: | 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. |
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| ISSN: | 2169-0375 |