Mathematics Colloquium - Xiang Xu
This event is in the past.
Detroit, MI 48202
Speaker: Professor Xiang Xu, Assistant Professor, Old Dominion Univeristy
Title: Strict/uniform physicality of a gradient flow generated by the anisotropic Landau-de Gennes energy with a singular potential
Abstract: We study a gradient flow generated by the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the Q-tensor space. This free energy density functional is composed of three quadratic terms as the elastic energy density part, and a singular potential in the bulk part that is considered as a natural enforcement of a physical constraint on the eigenvalues of Q. Specifically, we give a rigorous proof that if initially the Q-tensor is physical (with the free energy possibly being infinite), then it immediately becomes strictly physical as time evolves, and it becomes uniformly physical at all large times.