Global strong solutions to incompressible Ericksen–Leslie system in R3R3

In this paper, we consider the Cauchy problem to the Ericksen–Leslie system of liquid crystals in R3R3. Global well-posedness of strong solutions are obtained under the condition that the product of ‖u0‖2+‖∇d0‖2‖u0‖2+‖∇d0‖2 and ‖∇u0‖2+‖∇2d0‖2‖∇u0‖2+‖∇2d0‖2 is suitably small. This result can be viewed as a supplement to the local existence and blow up criteria, recently established in Hong et al. (2014).