Global existence for slightly compressible hydrodynamic flow of liquid crystals in two dimensions  

作　　者：DING ShiJin HUANG JinRui LIN JunYu 

机构地区：[1]School of Mathematical Sciences, South China Normal University [2]Department of Mathematics, South China University of Technology

出　　处：《Science China Mathematics》2013年第11期2233-2250,共18页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002);National Natural Science Foundation of China(Grant Nos.11001085,11071086 and 11128102);the University Special Research Foundation for PhD Program(Grant No.20104407110002);the PhD Programs Foundation of Ministry of Education of China(Grant No.20100172120026);the Fundamental Research Funds for the Central Universities(Grant No.2012ZZ0075)

摘　　要：In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. （2013）, when the parameter λ→∞ oo, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, Ding et al. （2013） proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that is sufficiently large and the initial data are almost incompressible.In two dimensions,we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions.As shown by Ding et al.(2013),when the parameterλ→∞,the solutions to the compressible liquid crystal system approximate that of the incompressible one.Furthermore,Ding et al.(2013)proved that the regular incompressible limit solution is global in time with small enough initial data.In this paper,we show that the solution to the compressible liquid crystal flow also exists for all time,provided thatλis sufciently large and the initial data are almost incompressible.

关 键 词：liquid crystals slightly compressible global existence 

分 类 号：O357[理学—流体力学]