abstract: We study the global well-posedness of the 3-D Navier-Stokes equations for a class of large initial data. This type of data slowly varies in the vertical direction and it is ill-prepared in the sense that its norm blows up when the small parameter converges to zero. We prove the global well-posedness for large initial data with Gevrey regularity. The talk is based on joint works with Jean-Yves Chemin, Isabelle Gallagher and Zhifei Zhang.