Global existence of solutions to 2-D Navier–Stokes flow with non-decaying initial data in half-plane

Abstract

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-dimensional 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.