On the free-boundary Incompressible Elastodynamics with and without surface tension
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909376032276480 |
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| author | Xu, Longhui |
| author_facet | Xu, Longhui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the free-boundary Incompressible Elastodynamics with and without surface tension Xu, Longhui Analysis of PDEs 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. |
| title | On the free-boundary Incompressible Elastodynamics with and without surface tension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.01124 |