Long-time behavior of solutions to the compressible liquid crystals

Abstract

In this paper, we consider the long-time behavior of the liquid crystals equations of compressible flow. We prove that if the static state ds minimizes the Ginzburg-Landau approximation energy, then the finite energy weak solutions (ρ, u, d)(t, x) converges to (ρs, 0, ds)(x) with unique density function ρs, which satisfies the conservation of mass.