Geodesic
The Cauchy problem for the liquid crystals system in the critical Besov space with negative index
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 37-55.

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The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space $\dot {B}_{p,1}^{n/p-1}(\mathbb R^n)\times \dot {B}_{p,1}^{n/p}(\mathbb R^n)$ with $n$ is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed.
DOI : 10.21136/CMJ.2017.0249-15
Classification : 35B44, 35Q35, 76A15
Keywords: liquid crystals system; critical Besov space; negative index; well-posedness; blow-up 
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Ming, Sen; Yang, Han; Chen, Zili; Yong, Ls. The Cauchy problem for the liquid crystals system in the critical Besov space with negative index. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 1, pp. 37-55. doi : 10.21136/CMJ.2017.0249-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0249-15/

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