BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index
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Authors
Baoquan Yuan
- School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China.
Chengzhou Wei
- School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China.
Abstract
In this paper, we investigate the blow-up criterion of a smooth solution of the nematic liquid crystal flow in threedimensional
space. More precisely, We prove that if
\(\int^T_0(\|\omega\|^{\frac{2}{2-\alpha}}_{\dot{B}^{-\alpha}_{\infty,\infty}}+\|\nabla d\|^2_{\dot{B}^0_{\infty,\infty}})dt<\infty, 0<\alpha<2,\) then the solution \((u, d)\)
can be extended smoothly beyond \(t = T\).
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ISRP Style
Baoquan Yuan, Chengzhou Wei, BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 3030--3037
AMA Style
Yuan Baoquan, Wei Chengzhou, BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index. J. Nonlinear Sci. Appl. (2017); 10(6):3030--3037
Chicago/Turabian Style
Yuan, Baoquan, Wei, Chengzhou. "BKM's criterion for the 3D nematic liquid crystal flows in Besov spaces of negative regular index." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 3030--3037
Keywords
- Nematic liquid crystal flow
- blow-up criteria
- regularity criteria
- Besov space.
MSC
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