Global existence of solutions for the second grade fluid equations in a thin three-dimensional domain

We consider the second grade fluid equations on a thin three-dimensional domain with periodic boundary conditions. We prove global existence and uniqueness of the solution for large initial data. We use an appropriate decomposition of solution u into a v part, which is solution of a 2D second grade fluid equations and the remaining w part which has an initial data converging to 0 as the thickness of the thin domain goes to 0.