Local well-posedness to the 2D Cauchy problem of non-isothermal nonhomogeneous nematic liquid crystal flows with vacuum at infinity

Hong Chen; Xin Zhong

doi:10.3934/cpaa.2022093

Article Contents

2022, Volume 21, Issue 9: 3141-3169. Doi: 10.3934/cpaa.2022093

This issue Previous Article Systems of semilinear wave equations with multiple speeds in two space dimensions and a weaker null condition Next Article Application of the nonlinear steepest descent method to the general coupled nonlinear Schrödinger system

Local well-posedness to the 2D Cauchy problem of non-isothermal nonhomogeneous nematic liquid crystal flows with vacuum at infinity

Hong Chen and
Xin Zhong^,

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

^* Corresponding author
^* Corresponding author

Received: January 31, 2022

Revised: March 31, 2022

Early access: May 2022

Published: September 2022

This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359) and Exceptional Young Talents Project of Chongqing Talent (No. cstc2021ycjh-bgzxm0153)

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Abstract

This paper concerns the Cauchy problem of non-isothermal nonhomogeneous nematic liquid crystal flows in $ \mathbb{R}^2 $ with zero density at infinity. By spatial weighted energy method and a Hardy type inequality, we show the local existence and uniqueness of strong solutions provided that the initial density and the gradient of orientation decay not too slowly at infinity.

Keywords:

Non-isothermal nonhomogeneous nematic liquid crystal flows,
local well-posedness,
2D Cauchy problem,
vacuum at infinity.

Mathematics Subject Classification: Primary: 76A15; Secondary: 76D03.

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References

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