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 $u_0\in L^{\infty }(R_{+}^2)\cap J_0^2(R_{+}^2)$ or with non decaying initial data $u_0\in L^{\infty }(R_{+}^2)\cap J_0^p(R_{+}^2),p>2$ . 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.

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