  We study a fictitious domain approach with Lagrange multipliers to discretize
Stokes equations on a mesh that does not fit the boundaries. A mixed finite
element method is used for fluid flow. Several stabilization terms are added to
improve the approximation of the normal trace of the stress tensor and to avoid
the inf-sup conditions between the spaces of the velocity and the Lagrange
multipliers. We generalize first an approach based on eXtended Finite Element
Method due to Haslinger-Renard involving a Barbosa-Hughes stabilization and a
robust reconstruction on the badly cut elements. Secondly, we adapt the
approach due to Burman-Hansbo involving a stabilization only on the Lagrange
multiplier. Multiple choices for the finite elements for velocity, pressure and
multiplier are considered. Additional stabilization on pressure
(Brezzi-Pitk\"aranta, Interior Penalty) is added, if needed. We prove the
stability and the optimal convergence of several variants of these methods
under appropriate assumptions. Finally, we perform numerical tests to
illustrate the capabilities of the methods.
