Stability of the tumbled state in shear flow of a nematic liquid crystal

In shear flow of a nematic liquid crystal with₃ 0 flow alignment cannot occur. The stability of the stationary in-plane solution, the tumbled state, is investigated using abstract techniques. Employing the existence of an elastic energy a sufficient criterion for stability is formulated. This criterion depends on the in-plane solution which is obtainable as a quadrature that is non-elementary except in special cases. It is shown that the tumbled state is stable and asymptotically stable for some physical configurations. The criterion presented is not a necessary condition for stability and thus only gives a lower bound.