  This paper gives another version of results due to Raugel and Sell, and
similar results due to Moise, Temam and Ziane, that state the following: the
solution of the Navier-Stokes equation on a thin 3 dimensional domain with
periodic boundary conditions has global regularity, as long as there is some
control on the size of the initial data and the forcing term, where the control
is larger than that obtainable via ``small data'' estimates. The approach taken
is to consider the three dimensional equation as a perturbation of the equation
when the vector field does not depend upon the coordinate in the thin
direction.
