On a 3D isothermal model for nematic liquid crystals accounting for stretching terms
On a 3D isothermal model for nematic liquid crystals accounting for stretching terms
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DOI：
10.1007/s00033-012-0219-7
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
C. Cavaterra;E. Rocca
中科院分区：
文献类型：
--
作者：
C. Cavaterra;E. Rocca
在本文中，我们研究了一个PDE系统，描述了不同形状分子在运动输运下向列液晶流动的演变。更具体地说，速度场的演化由Navier-Stokes不可压缩系统控制，该系统具有在输运项和诱导项之间表现出特殊耦合的应力张量。通过对物理约束|d| = 1的适当惩罚，用抛物线型金兹堡-朗道方程的变化来描述定向场的动力学。该方程既考虑了流场的运动输运，又考虑了弹性能引起的内部松弛。这一贡献的主要目的是克服指挥方程的最大原理的缺乏，并证明（不受数据和问题的物理常数的任何限制）在物理上有意义的边界条件下的全局时间弱解的存在。
In the present contribution, we study a PDE system describing the evolution of a nematic liquid crystals flow under kinematic transports for molecules of different shapes. More in particular, the evolution of thevelocity fielduis ruled by the Navier–Stokes incompressible system with a stress tensor exhibiting a special coupling between the transport and the induced terms. The dynamics of thedirector fielddis described by a variation of a parabolic Ginzburg–Landau equation with a suitable penalization of the physical constraint |d| = 1. Such equation accounts for both the kinematic transport by the flow field and the internal relaxation due to the elastic energy. The main aim of this contribution is to overcome the lack of a maximum principle for the director equation and prove (without any restriction on the data and on the physical constants of the problem) the existence of global in time weak solutions under physically meaningful boundary conditions ondandu.