arXiv subjects

Longhui Xu

Publications and source records attributed to Longhui Xu.

2 recordsLinked to original sources

arXiv2024

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

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.

math.AP↗

arXiv2024

On the free-boundary Incompressible Elastodynamics with and without surface tension

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.

math.AP↗