Local Well-posedness of the Free-boundary Problem in Incompressible Elastodynamics with Surface Tension

Fuente: arXiv
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Main Author: Xu, Longhui
Format: Preprint
Published: 2024
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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