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| GLOBAL EXISTENCE AND LONG-TIME BEHAVIOR FOR THE STRONG SOLUTIONS IN H2 TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS |
| Jincheng Gao,Boling Guo,Xiaoyu Xi |
| (Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P.R. of China;The Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing, 100088, P.R. of China) |
| DOI： |
| Abstract: |
| In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in three-dimensional whole space.
The global existence of strong solutions is obtained by the standard energy method under the condition that the initial datas are close to the constant equilibrium state in H2-framework. If the initial datas in L1-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director. |
| Key words: ompressible nematic liquid crystal flows; global solution; Green function; long-time behavior |