On the free-boundary Incompressible Elastodynamics with and without surface tension

2024/11/02 by Lu Xu, Xu, Longhui
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2411.01124

openalex publication_date 2024/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local well-posedness in Lagrangian coordinates is proved by extending arXiv:2105.00596 on incompressible magnetohydrodynamics. We adapt the idea in arXiv:2211.03600 on compressible gravity-capillary water waves to obtain an energy estimate in graphic coordinates. The energy estimate is uniform in surface tension coefficient if the Rayleigh-Taylor sign condition holds and thus yields the zero-surface-tension limit.

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