Oberseminar Mathematik in den Naturwissenschaften: Francesco de Anna, Recent developments on the Ericksen-Leslie theory for the flow of nematic liquid crystals

The Ericksen-Leslie system is a fundamental hydrodynamic model that describes the evolution of incompressible liquid crystal flows of nematic type. In this talk we present a recent result concerning the general Ericksen-Leslie system with a Ginzburg-Landau type approximation.

Up until recently, a fundamental problem that had remained open was the uniqueness of weak solutions. The essential mathematical difficulties of the model arise indeed from highly non-linear terms and a lack of maximum principle due to the stretching effect of the fluid on the constitutive molecules. In this talk we present a recent result which provides a positive answer to the uniqueness problem of weak solutions in a two-dimensional periodic domain.

We introduce a specific toolbox of Fourier Analysis, in order to address the mentioned result.