Existence and Uniqueness Theorems for the Two-Dimensional Ericksen–Leslie System

Gregory A. Chechkin (1) , Tudor S. Ratiu (2, 3) , Maxim S. Romanov (1) , Vyacheslav N. Samokhin (4)

1 Department of Differential Equations
2 EPFL - Ecole Polytechnique Fédérale de Lausanne
3 Department of Mathematics, Jiao Tong University
4 Moscow State University of Printing Art 2A, Moscow

In this paper we study the two dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value problem in two situations: the space-periodic problem and the case of a bounded domain with spatial Dirichlet boundary conditions on the Eulerian velocity and the cross product of the director field with its time derivative. We also show that the speed of propagation of the director field is finite and give an upper bound for it.

Domaines: Mathématiques [math]

Gregory A. Chechkin, Tudor S. Ratiu, Maxim S. Romanov, Vyacheslav N. Samokhin. Existence and Uniqueness Theorems for the Two-Dimensional Ericksen–Leslie System. Journal of Mathematical Fluid Mechanics, 2016, 18 (3), pp.571-589. ⟨hal-01383845⟩