Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces. This is partially joint work with J. Y. Chemin, Guilong GUI and M. Paicu.