Line defects in the vanishing elastic constant limit of a three-dimensional Landau-de Gennes model

Giacomo Canevari (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We consider the Landau-de Gennes variational model for nematic liquid crystals, in three-dimensional domains. We are interested in the asymptotic behaviour of minimizers as the elastic constant tends to zero. Assuming that the energy of minimizers is bounded by the logarithm of the elastic constant, there exists a relatively closed, 1-rectiable set S line of nite length, such that minimizers converge to a locally harmonic map away from S line. We provide sucient conditions for the logarithmic energy bound to be satised. Finally, we show by an example that the limit map may have both point and line singularities.

Keywords: Landau-de Gennes model; Q-tensors; asymptotic analysis; topological singularities; line defects; rectiable sets

Domains: Analysis of PDEs [math.AP]

Giacomo Canevari. Line defects in the vanishing elastic constant limit of a three-dimensional Landau-de Gennes model. 2015. ⟨hal-01157753⟩