Global weak solution and large-time behavior for the compressible flow of liquid crystals

Abstract

The three-dimensional equations for the compressible flow of liquid crystals are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent ${\hat{I}}^3>\frac{3}{2}$.