Torus vs split solutions for the Landau de Gennes model

par Adriano Pisante (U di Roma La Sapienza)

lundi 16 juin 2025, 14:00 → 15:00 Europe/Paris

Salle Pellos (1R2-203)

We report on some recent works (in collaboration with F. Dipasquale and V.Millot) about the study of global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals in three-dimensional domains. First, we discuss absence of singularities for minimizing configurations under norm constraint, as well as absence of the isotropic phase for the unconstrained minimizers, together with the topological character of the related biaxial escape phenomenon. Then, we discuss the previous properties under both the norm and the axial symmetry constraints, showing that in this case only partial regularity is available, away from a finite set located on the symmetry axis where we describe precisely the asymptotic profile around singular points. Moreover, we discuss presence/absence/coexistence of smooth and singular minimisers  in a fixed symmetric domain as the boundary data vary. Finally, the same properties are investigated under radial anchoring when the domain is suitably deformed.