Volume 27, Issue 3
Liquid Crystal Flows with Regularity in One Direction
10.4208/jpde.v27.n3.5

J. Part. Diff. Eq., 27 (2014), pp. 245-250.

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• Abstract

In this paper, we consider the Cauchy problem for the model of liquid crystal. We show that if the velocity field u satisfies $$∂_3u∈L^p(0,T;L^q(\mathbb{R}^3)), \frac{2}{p}+\frac{3}{q}+=1+\frac{1}{q}, 2 ‹ q ≤ ∞,$$ then the solution is in fact smooth.

• History

Published online: 2014-09

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