Decay estimates for three-dimensional nematic liquid crystal system

Xiufang Zhao; Xiufang Zhao

doi:10.3934/math.2022887

AIMS Mathematics

2022, Volume 7, Issue 9: 16249-16260. doi: 10.3934/math.2022887

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Research article

Decay estimates for three-dimensional nematic liquid crystal system

Xiufang Zhao ^,

School of Science, Qiqihar University, Qiqihar 161006, China

Received: 22 April 2022 Revised: 25 June 2022 Accepted: 29 June 2022 Published: 04 July 2022
MSC : 35Q35, 76D03, 35B40

In this paper, we consider the decay rates of the higher-order spatial derivatives of solution to the Cauchy problem of 3D compressible nematic liquid crystals system. The $ \dot{H}^s\; (\frac12 < s < \frac32) $ negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.
- nematic liquid crystals,
- Ericksen-Leslie system,
- energy estimates,
- negative Sobolev space,
- decay estimates
Citation: Xiufang Zhao. Decay estimates for three-dimensional nematic liquid crystal system[J]. AIMS Mathematics, 2022, 7(9): 16249-16260. doi: 10.3934/math.2022887

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Abstract

In this paper, we consider the decay rates of the higher-order spatial derivatives of solution to the Cauchy problem of 3D compressible nematic liquid crystals system. The $ \dot{H}^s\; (\frac12 < s < \frac32) $ negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.

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