Volume 27, Issue 3
Liquid Crystal Flows with Regularity in One Direction

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

Published online: 2014-09

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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.

• Keywords

Liquid crystals regularity criteria

35Q35 76B03

@Article{JPDE-27-245, author = {}, title = {Liquid Crystal Flows with Regularity in One Direction}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {3}, pages = {245--250}, 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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/5140.html} }
TY - JOUR T1 - Liquid Crystal Flows with Regularity in One Direction JO - Journal of Partial Differential Equations VL - 3 SP - 245 EP - 250 PY - 2014 DA - 2014/09 SN - 27 DO - http://dor.org/10.4208/jpde.v27.n3.5 UR - https://global-sci.org/intro/jpde/5140.html KW - Liquid crystals KW - regularity criteria AB - 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.