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We consider the two-dimensional Landau-de Gennes energy with several elasticconstants, subject to general $k$-radially symmetric boundary conditions. Weshow that for generic elastic constants the critical points consistent with thesymmetry of the boundary conditions exist only in the case $k=2$. In this casewe identify three types of radial profiles: with two, three of full fivecomponents and numerically investigate their minimality and stability dependingon suitable parameters. We also numerically study the stability properties ofthe critical points of the Landau-de Gennes energy and capture the intricatedependence of various qualitative features of these solutions on the elasticconstants and the physical regimes of the liquid crystal system.

Liquid crystal defects in the Landau-de Gennes theory in two dimensions-beyond the one-constant approximation