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This article is concerned with the rigorous connections between the inertialQian--Sheng model and the Ericksen--Leslie model for the liquid crystal flow,under a more general condition of coefficients. More specifically, in theframework of Hilbert expansions, we show that: (i) when the elasticcoefficients tend to zero (also called the uniaxial limit), the smooth solutionto the inertial Qian--Sheng model converges to that to the full inertialEricksen--Leslie model; (ii) when the elastic coefficients and the inertialcoefficient tend to zero simultaneously, the smooth solution to the inertialQian--Sheng model converges to that to the noninertial Ericksen--Leslie model.

Rigorous uniaxial limit of the Qian--Sheng inertial Q-tensor hydrodynamics for liquid crystals