## Dynamic instability of the liquid crystal director.(English)Zbl 0702.35180

Current progress in hyperbolic systems: Riemann problems and computations, Proc. AMS-IMS-SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 100, 325-330 (1989).
[For the entire collection see Zbl 0683.00014.]
The study of nematic liquid crystals usually addresses the problem of investigating the behavior of at least two linearly independent vector fields. This paper emphasizes only one vector field namely the director field. A map, u(x,t), is termed a director if and only if it maps a subset of $${\mathbb{R}}^ 3\times [0,T]$$, $$T<\infty$$, into the two dimensional sphere. Such a special director map is carefully examined in the spirit of the Euler-Lagrange equation. The analysis is thoroughly developed and the behavior of the solution is carefully shown to be essentially hyperbolic of the exhibit a change of type. The eigenvalues and growth conditions for the system are analyzed. The paper is carefully developed and well organized.
Reviewer: J.Schmeelk

### MSC:

 35M10 PDEs of mixed type 82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)

Zbl 0683.00014