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The Cauchy problem for the liquid crystals system in the critical Besov space with negative index

Sen MingHan YangZili ChenLs Yong — 2017

Czechoslovak Mathematical Journal

The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space B ˙ p , 1 n / p - 1 ( n ) × B ˙ p , 1 n / p ( n ) with n < p < 2 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.

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