Analysis of a variational model for nematic shells

作者：Segatti Antonio^*; Snarski Michael; Veneroni Marco

来源：Mathematical Models and Methods in Applied Sciences, 2016, 26(10): 1865-1918.

DOI：10.1142/S0218202516500470

• Liquid crystals
• gradient-flow
• surface energy
• topological defects
• harmonic maps

We analyze an elastic surface energy which was recently introduced by G. Napoli and L. Vergori to model thin films of nematic liquid crystals. We show how a novel approach in modeling the surface's extrinsic geometry leads to considerable differences with respect to the classical intrinsic energy. Our results concern three connected aspects: (i) using methods of the calculus of variations, we establish a relation between the existence of minimizers and the topology of the surface; (ii) we prove, by a Ginzburg-Landau approximation, the well-posedness of the gradient flow of the energy; (iii) in the case of a parametrized torus we obtain a stronger characterization of global and local minimizers, which we supplement with numerical experiments.

• 出版日期2016-9