2013/08/19 by Changyou Wang, Xiang Xu, Wang, Changyou +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1308.4000
openalex publication_date 2013/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S2, namely the uniform convergence in L2 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 ωi(1≤ i≤ l) share a common orientation. As consequences, the uniformity property holds under various types of small initial data.