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Article

Ming, Sen ; Yang, Han ; Chen, Zili ; Yong, Ls
The Cauchy problem for the liquid crystals system in the critical Besov space with negative index. (English). Czechoslovak Mathematical Journal, vol. 67 (2017), issue 1, pp. 37-55
MSC: 35B44, 35Q35, 76A15 | MR 3632997 | Zbl 06738503 | DOI: 10.21136/CMJ.2017.0249-15
Keywords:
liquid crystals system; critical Besov space; negative index; well-posedness; blow-up
Summary:
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 $n<p<2n$ 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.
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