The Cauchy problem for the liquid crystals system in the critical Besov space with negative index
The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space with is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed.