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2001 Singularities and nonuniqueness in cylindrical flow of nematic liquid crystals
E. Vilucchi, R. van der Hout
Adv. Differential Equations 6(7): 799-820 (2001).

Abstract

The subject of this paper is the behavior of the director field of a nematic liquid crystal in flow through a tube with circular cross-section. Both the flow and the director field are assumed to have cylindrical symmetry. The requirement of finite Frank-Oseen energy forces ``admissible" director fields to be axially directed at the location of the symmetry axis. Thus, the angle between the axis and the director field at the location of the axis amounts to $k\pi$, $k$ being an integer. In the steady case, it is shown that $k$ is largely (but not uniquely) determined by the (Dirichlet) boundary conditions. In particular, this may give rise to line singularities with finite energy density. Moreover, the associated Dirichlet problem may have several distinct solutions with identical value of $k$. Analogously to the heat flow of harmonic mappings, finite-time blow-up phenomena for the associated parabolic problem are established.

Citation

Download Citation

E. Vilucchi. R. van der Hout. "Singularities and nonuniqueness in cylindrical flow of nematic liquid crystals." Adv. Differential Equations 6 (7) 799 - 820, 2001.

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1142.35380
MathSciNet: MR1828997

Subjects:
Primary: 35J20
Secondary: 35K55, 58E50, 76A15

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.6 • No. 7 • 2001
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