TY - JOUR
T1 - Global Existence and Long-Time Behavior for the Strong Solutions in $H^2$ to the 3D Compressible Nematic Liquid Crystal Flows
AU - Gao , Jincheng
AU - Guo , Boling
AU - Xi , Xiaoyu
JO - Annals of Applied Mathematics
VL - 4
SP - 331
EP - 356
PY - 2022
DA - 2022/06
SN - 32
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20648.html
KW - compressible nematic liquid crystal flows, global solution,
Green function, long-time behavior.
AB - <p style="text-align: justify;">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 data are
close to the constant equilibrium state in $H^2$-framework. If the initial data in $L^1$-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.</p>