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arXiv · 2411.14840

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

Longhui Xu
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Abstract

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 $\kappa > 0$ to boost the boundary regularity, which recovers the original system as $\kappa\to 0$, and the energy estimates yield no regularity loss.

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Longhui Xu. 2024-11-22. Local Well-posedness of the Free-boundary Problem in Incompressible Elastodynamics with Surface Tension. https://arxiv.org/abs/2411.14840

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