We investigate the Navier-Stokes initial boundary value problem in the
half-plane R+2 with initial data u0∈L∞(R+2)∩J02(R+2)
or with non decaying initial data u0∈L∞(R+2)∩J0p(R+2),p>2 . We introduce a technique that allows to solve the two-dimesional
problem, further, but not least, it can be also employed to obtain weak
solutions, as regards the non decaying initial data, to the three-dimensional
Navier-Stokes IBVP. This last result is the first of its kind