Local Well-posedness of the Free-boundary Problem in Incompressible Elastodynamics with Surface Tension
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910774998335488 |
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| author | Xu, Longhui |
| author_facet | Xu, Longhui |
| contents | We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity. We adapt the idea in arXiv:2312.11254 to generate an approximate problem with artificial viscosity indexed by $κ> 0$ to boost the boundary regularity, which recovers the original system as $κ\to 0$, and the energy estimates yield no regularity loss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14840 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Well-posedness of the Free-boundary Problem in Incompressible Elastodynamics with Surface Tension Xu, Longhui Analysis of PDEs We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity. We adapt the idea in arXiv:2312.11254 to generate an approximate problem with artificial viscosity indexed by $κ> 0$ to boost the boundary regularity, which recovers the original system as $κ\to 0$, and the energy estimates yield no regularity loss. |
| title | Local Well-posedness of the Free-boundary Problem in Incompressible Elastodynamics with Surface Tension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.14840 |