  In this paper, we prove the local well-posedness of the Ericksen-Leslie
system, and the global well-posednss for small initial data under the physical
constrain condition on the Leslie coefficients, which ensures that the energy
of the system is dissipated. Instead of the Ginzburg-Landau approximation, we
construct an approximate system with the dissipated energy based on a new
formulation of the system.
