On the rigidity of nematic liquid crystal flow on S 2

摘要

In this paper we establish the uniformity property of a simplified Ericksen-Leslie system modelling the hydrodynamics of nematic liquid crystals on the two-dimensional unit sphere S 2, namely the uniform convergence in L 2 to a steady state exponentially as t tends to infinity. The main assumption, similar to Topping [15], concerns the equation of liquid crystal director d and states that at infinity time, a weak limit d∞ and any bubble ω_i (1 ≤ i ≤ 1) share a common orientation. As a consequence, the uniformity property holds under various types of small initial data.