On the $(x,t)$ asymptotic properties of solutions of the Navier-Stokes equations in the half-space.

Abstract: We get results of existence and of uniqueness of solutions assuming that at initial data has a suitable spatial behaviour. We study pointwise stability and asymptotic behaviour in (t,x) variables of the solutions. The region of the motion is the half space and the solutions can be with non finite kinetic energy. The difficulty is connected with the fact that the Green function is expressed by a convolution product between the heat kernel and the fundamental solutions of Laplace equation.