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Research Article | Open Access

Decay estimates for three-dimensional nematic liquid crystal system

School of Science, Qiqihar University, Qiqihar 161006, China
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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 H ˙ s ( 1 2 < s < 3 2 ) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.

Keywords

nematic liquid crystalsEricksen-Leslie systemenergy estimatesnegative Sobolev spacedecay estimates
CLC number: 35Q35, 76D03, 35B40

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16249-16260
DOI: 10.3934/math.2022887

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Zhao X. Decay estimates for three-dimensional nematic liquid crystal system. AIMS Mathematics, 2022, 7(9): 16249-16260. https://doi.org/10.3934/math.2022887

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Received: 22 April 2022
Revised: 25 June 2022
Accepted: 29 June 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)