Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals

Abstract

We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the $Q$-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical effects produced by the presence of this cubic term by considering an $L^2$ gradient flow generated by this energy. We work in two dimensions and concentrate on understanding the relations between the physicality of the initial data and the global well-posedness of the system.

References in corpus (2)

• Introduction to Q-tensor theory
• Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential