Spatial decay of Navier-Stokes flow in aperture domains with time depending flux

In this paper, we consider the initial boundary value problem for the Navier-Stokes equations in an aperture domain , there are several related results. We furnish the spatial asymptotic behavior of solutions corresponding to a flux F(t) (here F(t)denotes the flux through the aperture M, that is 2-dimensional manifold). The flux F(t) is assumed only bounded for t > 0. In a recent paper it is proved that to small fluxes F(t) and to small initial data there correspond, defined for any t > 0, smooth solutions of the Navier-Stokes problem in an aperture domain . Here we study the spatial behavior of these solutions in two special cases when the initial data either vanish or have a suitable spatial decay rate.