PDE problems in the Landau-de Gennes theory for Nematic Liquid Crystals

Abstract: Nematic liquid crystals are classical examples of partially ordered materials that combine fluidity with the order of crystalline solids. Nematics have long-range orientational order i.e. they are directional materials with special directions, referred to as directors. The Landau-de Gennes theory is one of the most celebrated and powerful continuum theories for nematic liquid crystals. In this talk, we review the mathematical framework for the Landau-de Gennes theory with emphasis on the Landau-de Gennes free energy and the associated Euler-Lagrange equations, which are typically a system of coupled, nonlinear partial differential equations. We review some recent results for boundary-value problems in the Landau-de Gennes theory, including results on the multiplicity, defect sets and asymptotic analysis of energy-minimizing solutions. We also describe the physical relevance of these solutions, followed by case studies of applications in the physical sciences and industry.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

"Partial Differential Equations and Applications" Webinar