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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Bibliographic Details
Main Author: Xie Binqiang
Format: Article
Language:English
Published: De Gruyter 2025-01-01
Series:Advanced Nonlinear Studies
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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.
ISSN:2169-0375