Global existence of strong solutions to micropolar equations in cylindrical domains

Abstract

The micropolar equations are a useful generalization of the classical Navier-Stokes model for fluids with micro-structure. We prove the existence of global and strong solutions to these equations in cylindrical domains in ${\mathbb{R}}^3$. We do not impose any restrictions on the magnitude of the initial and external data but we require that they cannot change in the $x_3$-direction too fast.