Long-time behavior of solution for the compressible nematic liquid crystal flows in R-3
Long-time behavior of solution for the compressible nematic liquid crystal flows in R-3
复制标题
R-3 中可压缩向列液晶流动溶液的长期行为
DOI：
10.1016/j.jde.2016.04.033
复制
发表时间：
2016
影响因子：
2.4
通讯作者：
Tao Qiang
中科院分区：
文献类型：
--
作者：
Gao Jincheng;Yao Zheng-an;Tao Qiang
本文研究了三维全空间中可压缩双折射液晶流经典解的整体存在性和长时间性态。首先，在HN（R3）（N≥ 3）-框架下，在初值接近常数平衡态的条件下，证明了经典解的整体存在性。然后，利用能量加权法建立了经典解的代数时间衰减。最后，当初始扰动附加地属于L1（R3）时，得到了经典解在Lp（R3）-范数（其中2≤ p≤∞）下的代数衰减率及其空间导数在L2（R3）-范数下的最优衰减率.
In this paper, we investigate the global existence and long-time behavior of classical solution for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in H N (R 3)(N≥ 3)-framework. Then, one establishes algebraic time decay for the classical solution by weighted energy method. Finally, the algebraic decay rate of classical solution in L p (R 3)-norm with 2≤ p≤∞ and optimal decay rate of their spatial derivative in L 2 (R 3)-norm are obtained if the initial perturbation belong to L 1 (R 3) additionally.