Sufficient conditions for stability of shear flow of nematic liquid crystals

In this paper we investigate the role of Parodi's relation in the stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. For shear flow of nematic liquid crystals, Wu, Xu and Liu have shown that if Parodi's relation does not hold, the Ericksen-Leslie system may be linearly unstable. Assuming Parodi's relation and adding a restriction on the alignment of the molecules via Leslie coefficients, we show in this work that the Ericksen-Leslie system satisfies the stablity condition for shear flow of nematic liquid crystals. © 2013 by CESER Publications.