A new blowup criterion for strong solutions of the compressible nematic liquid crystal flow

Sili Liu; Xinhua Zhao; Yingshan Chen

doi:10.3934/dcdsb.2020110

Article Contents

2020, Volume 25, Issue 11: 4515-4533. Doi: 10.3934/dcdsb.2020110

This issue Previous Article Almost sure exponential stabilization and suppression by periodically intermittent stochastic perturbation with jumps Next Article

A new blowup criterion for strong solutions of the compressible nematic liquid crystal flow

School of Mathematics, South China University of Technology, Guangzhou 510641, China

^* Corresponding author: Yingshan Chen
^* Corresponding author: Yingshan Chen

Received: February 28, 2019

Revised: September 30, 2019

Early access: March 2020

Published: November 2020

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Abstract

In this paper, we establish a new blowup criterion for the strong solution to the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a bounded domain $ \Omega\subset\mathbb{R}^{3} $. Specifically, we obtain the blowup criterion in terms of $ \|P\|_{L^\infty_t BMO_{x}} $ and $ \|\nabla d\|_{L^s_t L^\infty_x} $, for any $ s>3 $. The appearance of vacuum could be allowed.

Keywords:

Compressible nematic liquid crystal flows,
strong solution,
blowup criterion,
BMO norm.

Mathematics Subject Classification: Primary: 35Q35, 35D35; Secondary: 76N10.

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