Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 37-55, 2017
The Cauchy problem for the liquid crystals system in the critical Besov space with negative index
Sen Ming, Han Yang, Zili Chen, Ls Yong
Received May 13, 2015. First published February 24, 2017.
Abstract: 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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Affiliations: Sen Ming, Han Yang, Zili Chen, Department of Mathematics, Southwest Jiaotong University, Two Ring Road, No. 111, Chengdu, 610031, Sichuan, China, e-mail: hanyang95@263.net; Ls Yong, Department of Mathematics, Southwestern University of Finance and Economics, Guanghua Village Street, No. 55, Chengdu, 611130, Sichuan, China
