Global strong solution to the three-dimensional liquid crystal flows of Q-tensor model
Global strong solution to the three-dimensional liquid crystal flows of Q-tensor model
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DOI：
10.1016/j.jde.2016.10.011
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发表时间：
2016-01
影响因子：
2.4
通讯作者：
Yao Xiao
中科院分区：
文献类型：
--
作者：
Yao Xiao
研究了一个复杂的流体动力学系统，该系统模拟 R 3 有界域中向列液晶的流体。该系统是一个强制不可压缩纳维-斯托克斯方程与 Q 张量抛物线型方程的耦合。如果初始 Q 张量不是太“狂野”，我们在 Besov 空间中调用 Stokes 算子和抛物线算子的最大正则性来获得局部强解。此外，结果表明，如果初始数据是围绕平凡平衡状态的足够小的扰动，则这种解决方案可以扩展到全局解决方案。最后，证明这里获得的全局强解与Paicu和Zarnescu [26]中获得的弱解相同。
A complex hydrodynamic system that models the fluid of nematic liquid crystals in a bounded domain in R 3 is studied. The system is a forced incompressible Navier–Stokes equation coupled with a parabolic type equation of Q-tensors. We invoke the maximal regularity of the Stokes operators and parabolic operators in Besov spaces to obtain the local strong solution if the initial Q-tensor is not too “wild”. In addition, it is showed that such solution can be extended to a global one if the initial data is a sufficiently small perturbation around the trivial equilibrium state. Finally, it is proved that the global strong solution obtained here is identical to those weak solutions obtained in Paicu and Zarnescu [26].