Abstract
The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space \(\dot B_{p,1}^{n/p - 1}\left( {{\mathbb{R}^n}} \right) \times \dot B_{p,1}^{n/p}\left( {{\mathbb{R}^n}} \right)\) 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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The research has been supported by the National Natural Science Foundation of P.R. China (11471263) and Fundamental Research Funds for the Central Universities (SWJTU12CX061 and SWJTU09ZT36).
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Ming, S., Yang, H., Chen, Z. et al. The Cauchy problem for the liquid crystals system in the critical Besov space with negative index. Czech Math J 67, 37–55 (2017). https://doi.org/10.21136/CMJ.2017.0249-15
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DOI: https://doi.org/10.21136/CMJ.2017.0249-15