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.

arXiv comment29 pages

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