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Sufficient Conditions for Stability of Shear Flow of Nematic Liquid Crystals

Bagisa Mukherjee

Abstract



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.

Keywords


Nematic liquid crystals, Parodi’s relation, Shear flow, Stability.

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