Global well posedness for a Q-tensor model of nematic liquid crystals

Abstract

In this paper, we prove the global well posedness and the decay estimates for a $\mathbb{Q}$-tensor model of nematic liquid crystals in ${\mathbb{R}}^N$, $N\ge 3$. This system is coupled system by the Navier-Stokes equations with a parabolic-type equation describing the evolution of the director fields $\mathbb{Q}$. The proof is based on the maximal $L_p$ -$L_q$ regularity and the $L_p$ -$L_q$ decay estimates to the linearized problem.

29 pages

References in corpus (2)

• Equilibrium order parameters of liquid crystals in the Landau-De Gennes theory
• New thought on Matsumura-Nishida theory in the $L_p$-$L_q$ maximalregularity framework