The 3D liquid crystal system with Cannone type initial data and large vertical velocity

Abstract

The hydrodynamic theory of the nematic liquid crystals was established by Ericksen [4] and Leslie [8]. In this paper, based on a new technique, we obtain global well-posedness to a simplified model introduced by Lin [9] in the critical Besov space with Cannone type initial data and large vertical velocity, which improves the main result in [15]. In addition, the small condition on $u_0$ is independent of another small condition on $d_0-\bar{d}_0$, which is quite different from the previous works [15,16].