Abstract: In this talk, I will present different boundary conditions for the Stokes operator, relevant or not from the physical viewpoint. The general setting will be bounded open connected sets with Lipschitz boundary. The properties of the Stokes semigroup will be described. They will be used to prove existence in critical spaces of mild solutions of the incompressible Navier-Stokes system via a classical fixed point procedure. Uniqueness can be obtained in some cases via the property of maximal regularity.