Recent developments on the dynamics of nematic liquid crystals

par Francesco De Anna (Penn State University)

mardi 29 mai 2018, 15:15 → 16:15 Europe/Paris

Fokko Du Cloux (ICJ, Université Claude Bernard Lyon 1)

In this talk, we focus on some mathematical results arising from the study of anisotropic complex fluids, the motion of which is complicated by the existence of mesoscale structures. We address in particular some recent developments on the dynamics of liquid crystals, materials exhibiting both solids and liquids properties. The main peculiarity of these media is a privileged orientation of the constitutive molecules, which we investigate both in the director and the order tensor theories. The anisotropic coupling and competition within the structure of these materials are modelled within the framework of the energetic variational approach, which reveals the entire system of PDE’s driving the motion. We then analyse the related Cauchy problem, presenting some results of global well-posedness, regularity propagation and stability of equilibria. These results are especially based on Fourier-analysis techniques and the functional settings of Sobolev and Besov regularities.