Blow-up criterion for incompressible nematic type liquid crystal equations in three-dimensional space

Tariq Mahmood; Zhaoyang Shang; Tariq Mahmood; Zhaoyang Shang

doi:10.3934/math.2020051

AIMS Mathematics

2020, Volume 5, Issue 2: 746-765. doi: 10.3934/math.2020051

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Research article

Blow-up criterion for incompressible nematic type liquid crystal equations in three-dimensional space

Tariq Mahmood ¹,
Zhaoyang Shang ^{2
,
,}

1.
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
2.
School of Finance, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China

Received: 08 October 2019 Accepted: 19 December 2019 Published: 24 December 2019
MSC : 35B65, 35Q35, 76A15

In this paper, we consider two incompressible nematic type liquid crystal models in threedimensional space. Blow-up criterions for weak and smooth solutions are established in homogenous and nonhomogenous Besov space with negative regular index, respectively. As a result, we improve some previous results in Besov space.
- blow-up criterion,
- incompressible,
- liquid crystal equations,
- Besov space
Citation: Tariq Mahmood, Zhaoyang Shang. Blow-up criterion for incompressible nematic type liquid crystal equations in three-dimensional space[J]. AIMS Mathematics, 2020, 5(2): 746-765. doi: 10.3934/math.2020051

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Abstract

In this paper, we consider two incompressible nematic type liquid crystal models in threedimensional space. Blow-up criterions for weak and smooth solutions are established in homogenous and nonhomogenous Besov space with negative regular index, respectively. As a result, we improve some previous results in Besov space.

References

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