On the global well-posedness of strong dynamics of incompressible nematic liquid crystals in $${\mathbb{R}^N}$$ R N

Abstract

We consider the motion of a viscous incompressible liquid crystal flow in the N-dimensional whole space. We prove the global well-posedness of strong solutions for small initial data by combining the maximal \({L_p-L_q}\) regularities and \({L_p-L_q}\) decay properties of solutions for the Stokes equations and heat equations. As a result, we also proved the decay properties of the solutions to the nonlinear equations.