Wei Wang (Zhejiang University):
On the mean field limit of the Doi-Onsager model for liquid crystals
Time and place
Tuesday, 4.2.20, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
Abstract
The microscopic Doi-Onsager model is one of the most fundamental theories for liquid crystals. Formally, one can derive the macroscopic liquid crystals theories such as the Oseen-Frank/Ericksen-Leslie theory from it. We will discuss this issue in a rigorous framework. In particular, we show that when the typical molecular interaction distance tends to zero (called the mean field limit), minimizers or critical points of Onsager's energy functional converge to minimizing harmonic maps or weak harmonic maps respectively. If time permits, we will also show that, under the same limit, solutions of the dynamical Doi-Onsager equation without hydrodynamics will converge to weak solutions of the harmonic map heat flow, which can be viewed as a special Oseen-Frank gradient flow. These are based on joint works with Yuning Liu (NYU Shanghai).