Large time existence of strong solutions to micropolar equations in   cylindrical domains
  We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the fluid into account. We prove that under certain smallness assumption on the rate of change of the initial data and the external data there exists a unique and strong solution for any finite time $T$. 
B. Nowakowski
math.AP