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Volume 32, Issue 4
Global Existence and Long-Time Behavior for the Strong Solutions in $H^2$ to the 3D Compressible Nematic Liquid Crystal Flows

Jincheng Gao, Boling Guo & Xiaoyu Xi

Ann. Appl. Math., 32 (2016), pp. 331-356.

Published online: 2022-06

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  • 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 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.

  • Keywords

compressible nematic liquid crystal flows, global solution, Green function, long-time behavior.

  • AMS Subject Headings

35Q35, 35B40, 76A15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-32-331, author = {Gao , JinchengGuo , Boling and Xi , Xiaoyu}, title = {Global Existence and Long-Time Behavior for the Strong Solutions in $H^2$ to the 3D Compressible Nematic Liquid Crystal Flows}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {32}, number = {4}, pages = {331--356}, 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 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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20648.html} }
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 -

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.

Jincheng Gao, Boling Guo & Xiaoyu Xi. (2022). Global Existence and Long-Time Behavior for the Strong Solutions in $H^2$ to the 3D Compressible Nematic Liquid Crystal Flows. Annals of Applied Mathematics. 32 (4). 331-356. doi:
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