可压缩活性液晶模型的解的存在性

WELL-POSEDNESS FOR THE COMPRESSIBLE ACTIVE LIQUID CRYSTAL MODEL

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.