Large Ericksen number limit for the 2D general Ericksen–Leslie system

Abstract

In this paper, we address the issue of the so-called large Ericksen number limit for the general Ericksen–Leslie system of liquid crystals. By the standard nondimensionalization, we first prove that there exists a unique local smooth solution to the limiting system. Then we provide a qualitative estimate for the difference between the solutions of the general Ericksen–Leslie system and the limiting system, which corresponds to the partial decoupling effect in the limit of large Ericksen number.