可压缩活性液晶模型的解的存在性  

WELL-POSEDNESS FOR THE COMPRESSIBLE ACTIVE LIQUID CRYSTAL MODEL

作　　者：江宁 柯琳琳 宋晓宇[2] JIANG Ning;KE Lin-lin;SONG Xiao-yu(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;Chongqing Bashu Secondary School,Chongqing 400013,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072 [2]重庆市巴蜀中学,重庆400013

出　　处：《数学杂志》2023年第2期95-125,共31页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11971360)。

摘　　要：本文研究了基于Q-张量框架的可压缩活性液晶模型的流体动力学问题.在全空间或者圆环上,我们证明了模型的大初值局部经典解的存在性.并且,在一定的系数假设下,我们给出了在常数态附近圆环上小初值全局经典解的存在性.We consider the hydrodynamics of compressible flow of active liquid crystals model in the Q-tensor framework.The existence of local-in-time classical solution with large initial data in the whole space or torus is established.Furthermore,with an assumption on the coefficients,we also prove the global-in-time existence of classical solutions near a constant state with small initial data on the torus.

关 键 词：可压缩活性液晶模型 经典解 平衡态附近 全局时间 

分 类 号：O175.4[理学—数学]