Well-posedness of the free boundary problem in incompressible elastodynamics

TL;DR

This paper proves the local well-posedness of a free boundary problem in incompressible elastodynamics, demonstrating that elasticity stabilizes the Rayleigh-Taylor instability under certain conditions.

Contribution

It establishes the local well-posedness of the free boundary problem in incompressible elastodynamics with a natural stability condition, confirming elasticity's stabilizing effect.

Findings

Proves local well-posedness under a hyperbolicity condition

Shows elasticity stabilizes Rayleigh-Taylor instability

Provides rigorous mathematical confirmation of stability effects

Abstract

In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly hyperbolic. Our result gives a rigorous confirmation that the elasticity has a stabilizing effect on the Rayleigh-Taylor instability.