Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows

详细信息    查看全文

• 作者：Qiao Liu^a ; ^b ; ^{liuqao2005@163.com" class="auth_mail" title="E-mail the corresponding author} ; Shengquan Liu^b ; ^{shquanliu@163.com" class="auth_mail" title="E-mail the corresponding author} ; Wenke Tan^a ; ^c ; ^{tanwenkeybfq@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xin Zhong^c ; ^{xzhong1014@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：76A15 ; 35B65 ; 35Q35
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 December 2016
• 年：2016
• 卷：261
• 期：11
• 页码：6521-6569
• 全文大小：624 K

文摘

This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space R²${\mathbb{R}}^2$ with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admit a unique global strong solution provided that the initial data density and the gradient of orientation decay not too slow at infinity, and the initial orientation satisfies a geometric condition (see (1.3)). In particular, the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support. Furthermore, the large time behavior of the solution is also obtained.