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We consider a four-elastic-constant Landau-de Gennes energy characterizingnematic liquid crystal configurations described using the $Q$-tensor formalism.The energy contains a cubic term and is unbounded from below. We studydynamical 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 andconcentrate on understanding the relations between the physicality of theinitial data and the global well-posedness of the system.

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