Central China Normal University, Oct. 31-Nov. 1, 2014.
In this talk, I will show the a priori estimates of Sobolev norms for a free boundary problem of the incompressible neo-Hookean elastodynamics in two and three spatial dimensions by adopting a geometrical point of view of Christodoulou-Lindblad. Some estimates on the second fundamental form and velocity of the free surface are also obtained. This is based on a joint work with Professor D. Wang.