On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum

Yang Liu; Xin Zhong

doi:10.3934/cpaa.2020234

Article Contents

2020, Volume 19, Issue 11: 5219-5238. Doi: 10.3934/cpaa.2020234

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On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum

Yang Liu^1, and
Xin Zhong^2, ,

1.
College of Mathematics, Changchun Normal University, Changchun 130032, China
2.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author
^* Corresponding author

Received: February 29, 2020

Revised: May 31, 2020

Early access: September 2020

Published: November 2020

Yang Liu is supported by China Postdoctoral Science Foundation (No. 2018M642202) and National Natural Science Foundation of China (No. 11901288). Xin Zhong is supported by National Natural Science Foundation of China (No. 11901474)

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Abstract

This paper deals with the Cauchy problem of three-dimensional (3D) nonhomogeneous incompressible nematic liquid crystal flows. The global well-posedness of strong solutions with large velocity is established provided that $ \|\rho_0\|_{L^\infty}+\|\nabla d_0\|_{L^3} $ is suitably small. In particular, the initial density may contain vacuum states and even have compact support. Furthermore, the large time behavior of the solution is also obtained.

Keywords:

Nonhomogeneous incompressible nematic liquid crystal flows,
global strong solution,
vacuum.

Mathematics Subject Classification: Primary: 35D35, 35Q35; Secondary: 76A15; 76D03.

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References

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