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 make analysis in both the PDE and numeric aspects.

Professor Xiang Xu obtained PhD in mathematics from Pennsylvania State University in 2011. He joined Old Dominion University in 2015 and is now an assistant professor in the Department of Mathematics and Statistics. Prof. Xu's research interests are partial differential equations in general.