2024/11/22 by Lu Xu, Xu, Longhui
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2411.14840
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→ 0, and the energy estimates yield no regularity loss.