Global in time solution and time-periodicity for a smectic-A liquid crystal model
Global in time solution and time-periodicity for a smectic-A liquid crystal model
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DOI：
10.3934/cpaa.2010.9.1473
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发表时间：
2010-08
影响因子：
1
通讯作者：
B. Climent-Ezquerra;F. Guillén-González
中科院分区：
文献类型：
--
作者：
B. Climent-Ezquerra;F. Guillén-González
本文针对所谓的层变量$\varphi$（$\varphi$的水平集描述了近晶A液晶的层结构），获得了具有时间相关边界狄利克雷数据的近晶A液晶模型的一些结果。首先，考虑任意初始数据的初始边界问题，获得有界于无穷时间的弱解的存在性。其次，证明了时间周期弱解的存在性。然后，攻击全局时间规律性问题，获得两个问题（即初值问题和时间周期问题）的正则解（直到无穷大时间）的存在性和唯一性，但假设扩散张量的线性部分具有主导粘性系数。
In this paper some results are obtained for a smectic-A liquid crystal model with time-dependent boundary Dirichlet data for the so-called layer variable $\varphi$ (the level sets of $\varphi$ describe the layer structure of the smectic-A liquid crystal). First, the initial-boundary problem for arbitrary initial data is considered, obtaining the existence of weak solutions which are bounded up to infinity time. Second, the existence of time-periodic weak solutions is proved. Afterwards, the problem of the global in time regularity is attacked, obtaining the existence and uniqueness of regular solutions (up to infinity time) for both problems, i.e. the initial-valued problem and the time-periodic one, but assuming a dominant viscosity coefficient in the linear part of the diffusion tensor.