  We consider the stationary incompressible Navier-Stokes equation in the
half-plane with inhomogeneous boundary condition. We prove existence of strong
solutions for boundary data close to any Jeffery-Hamel solution with small flux
evaluated on the boundary. The perturbation of the Jeffery-Hamel solution on
the boundary has to satisfy a nonlinear compatibility condition which
corresponds to the integral of the velocity field on the boundary. The first
component of this integral is the flux which is an invariant quantity, but the
second, called the asymmetry, is not invariant, which leads to one
compatibility condition. Finally, we prove existence of weak solutions, as well
as weak-strong uniqueness for small data.
