Existence and Uniqueness Theorems in Two-Dimensional Nematodynamics. Finite Speed of Propagation

The paper is devoted to the two-dimensional Ericksen-Leslie system describing the nematodinamics of liquid crystals. The moment of inertia of molecules is supposed to be strictly positive. The existence of the solution was proved in the case of periodic domain and in the case of bounded domain. In the last case media is supposed to adhere to the solid surface, the director vector field describing orientation of the molecules is constant in the neighbourhood of the boundary. The uniqueness of the strong solution was proved in both cases. Also we prove the propagation of director disturbance has finite speed. This fact shows the difference between the model under consideration and models with zero moment of inertia of the molecules. The estimate of the speed of propagation depending on physical properties of the liquid crystal and the flow was obtained.