Global existence of Weak Solutions for a model of nematic liquid crystal-colloidal interactions

Abstract: In this paper we study a mathematical model describing the movement of a colloidal particle in a fixed, bounded three dimensional container filled with a nematic liquid crystal fluid. The motion of the fluid is governed by the Beris-Edwards model for nematohydrodynamics equations, which couples the incompressible Navier-Stokes equations with a parabolic system. The dynamics of colloidal particle within the nematic liquid crystal is described by the conservation laws of linear and angular momentum. We prove the existence of global weak solutions for the coupled system.