  Liquid crystal elastomers are special cross-linked polymer materials
combining the large elastic deformability of elastomers with the orientational
orders of liquid crystals. This model exhibits markedly different phenomena
than the liquid crystal model due to the strong coupling between mechanical
elastic deformation and orientation vector.
  Our results are threefold. (i) First we derive the hydrodynamics of liquid
crystal elastomers with inertial effect by energetic variational approach
inspired by Chun Liu [33]. (ii) Then we study the hyperbolic liquid crystal
elastomers from mathematical point, which is a fully quasilinear hyperbolic
system. The local well-posedness for large data is proved by zero-viscosity
limit method. (iii) Finally, we show the global regularity for small and smooth
initial data near the constant equilibrium in three dimensions, which is
achieved by carefully investigating the structure of second-order material
derivatives and the cancellations in the system. This is the first global
result on hyperbolic liquid crystal elastomers.
