On the 2D Ericksen-Leslie equations with anisotropic energy and external forces

In this paper we consider the 2D Ericksen-Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data. the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small. then we establish that the global weak solution does not have any singular times and is regular as long as the data are regular.

Automated summary

This paper considers the 2D Ericksen-Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy. Global weak solutions with finitely many singular times are proven under general assumptions, and it is also established that the global weak solution is regular as long as the data are regular and the initial data and external forces are sufficiently small.