  In this paper, we consider the stationary Stokes equations in an exterior
domain three-dimensional under a slip boundary condition without friction. We
set the problem in weighted Sobolev spaces in order to control the behavior at
infinity of the solutions. In this work, we try to investigate the existence
and uniqueness of the weak solutions related to this problem in $L^P-$theory
when $p>3$. Our proof are based on obtaining inf-sup conditions that play a
fundamental role.
