Disclinations in 3D Landau-de Gennes theory

In this talk I will introduce a new bifurcation theory to find multiple solutions of Landau-de Gennes equation. More precisely when subjected to the standard hedgehog boundary condition, we find two axially symmetric solutions beside the hedgehog one. One solution has biaxial torus structure, while another solution has split-core segment structure on z-axis. In the low-temperature limit, the work rigorously confirms various numerical and experimental results on the core-structure of solutions to the Landau-de Gennes equation.