Well-Posedness of the Free Boundary Problem in Elastodynamics with Mixed Stability Condition
Hui Li, Wei Wang, Zhifei Zhang · SIAM Journal on Mathematical Analysis · 2021
In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a mixed type stability condition, i.e., for each point of the free boundary, at least one of the Taylor sign condition $-\pa_np>0$ and the noncollinearity condition holds. This gives an affirmative answer to a problem raised by Trakhinin in [ J. Differential Equations, 264 (2018), pp. 1661--1715] for the incompressible case.