Strong solutions to the density-dependent incompressible nematic liquid crystal flows

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• 作者：Jincheng Gao^a ; ^{gaojc1998@163.com" class="auth_mail" title="E-mail the corresponding author} ; Qiang Tao^b ; ^{taoq060@126.com" class="auth_mail" title="E-mail the corresponding author} ; Zheng-an Yao^a ; ^{mcsyao@mail.sysu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q35 ; 76A15 ; 35D35 ; 35B44
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：260
• 期：4
• 页码：3691-3748
• 全文大小：573 K

文摘

In this paper, we investigate the density-dependent incompressible nematic liquid crystal flows in n  -dimensional (height="11" width="67" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022039615005902-si1.gif">$n=2\text{or}3$) bounded domain. The local existence and uniqueness of strong solutions are obtained when the viscosity coefficient of fluid depends on density. Furthermore, one establishes blowup criterions for the regularity of the strong solutions in dimensions two and three respectively. In particular, we build a blowup criterion just in terms of the gradient of density if the initial direction field satisfies some geometric configuration. For these results, the initial density need not be strictly positive.