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

Longhui Xu

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arXiv · 2411.01124

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

Longhui Xu

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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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Longhui Xu. 2024-11-02. On the free-boundary Incompressible Elastodynamics with and without surface tension. https://arxiv.org/abs/2411.01124

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