@article{Sun2022, 
author = {Junling Sun and Xuefeng Han},
title = {Existence of Sobolev regular solutions for the incompressible flow of liquid crystals in three dimensions},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {15759-15794},
keywords = {nematic liquid crystal flow, global Sobolev solution, asymptotic expansion},
url = {https://www.sciopen.com/article/10.3934/math.2022863},
doi = {10.3934/math.2022863},
abstract = {This paper considers a simplified three dimensional Ericksen-Leslie System for nematic liquid crystal flows in the unbounded domain    Ω  :=            R        +    ×            R        2   or the smooth bounded domain    Ω. The hydrodynamic system consists of the Navier-Stokes type equations for the fluid velocity coupled with a convective Ginzburg-Landau type equation for the averaged molecular orientation. We first establish the global existence of Sobolev regular solution with finite energies in Sobolev space        H          s        (  Ω  )  ×      H          s        (  Ω  ), where the index    s of the Sobolev space can be any large fixed integer, but    s  ≠  +  ∞. Then we give an asymptotic expansions of a family of Sobolev regularity solutions for such system in    Ω.}
}