Regularity of a Gradient Flow Generated by the Anisotropic Landau--de Gennes Energy with a Singular Potential

In this paper we study a gradient flow generated by the Landau--de Gennes free energy that describes nematic liquid crystal configurations in space of $Q$-tensors. This density functional is composed three quadratic terms as elastic part, and singular potential bulk part considered natural enforcement physical constraint on eigenvalues $Q$. The system nondiagonal parabolic with which trends to infinity logarithmically when $Q$ approach boundary. We give rigorous proof for rather general initial data possibly infinite energy, has unique strong solution after any positive time $t_0$. Furthermore, detaches from boundary sufficiently large $T_0$. also an estimate Hausdorff measure set where touches thus prove partial regularity result intermediate stage $(0,T_0)$.