Strict/Uniform Physicality of a Gradient Flow Generated by the Anisotropic Landau-de Gennes Energy with a Singular Potential

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.

Event Topic

Stochastic & Multiscale Modeling and Computation