Blow-up criterion for the 3D nematic liquid crystal flows via one velocity and vorticity components and molecular orientations

Abstract

In this paper, we are devoted to investigating the blow-up criteria for the three dimensional nematic liquid crystal flows. More precisely, we proved that the smooth solution $(u, d)$ can be extended beyond T, provided that $\int_{0}^{T}(||\omega_{3}||_{L^{p}}^{\frac{2p}{2p-3}}+||u_{3}||_{L^{q}}^{\frac{2q}{q-3}} +||\nabla d||_{\dot{B}_{\infty, \infty}^{0}}^{2})d t