Hydrostatic limit of the Navier-Stokes-alpha model

In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin striped domain. We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.
Comment: Premi{\`e}re version, 33 pages