  We prove the global stability of small perturbation near the the constant
equilibrium for the two dimensional simplified Ericksen-Leslie's hyperbolic
system for incompressible liquid crystal model, where the direction function of
liquid crystal molecules satisfies a wave map equation with an acoustical
metric. This improves the almost global existence result by Huang-Jiang-Zhao.
As byproducts, we obtain the sharp (same as the linear solution) decay
estimates for the nonlinear velocity and the nonlinear wave part. Moreover the
nonlinear wave part scatters to a linear solution as time goes to infinity.
  The main novelty of this paper is that we uncover a null structure inside the
velocity equation on the Fourier side for the nonlinear interaction between
nonlinear heat equation and nonlinear wave equation.
