On the Navier–Stokes equations in the half-space with initial and boundary rough data in Morrey spaces

We consider the initial–boundary value problem for the Navier–Stokes equations in the half-space with data in Morrey spaces. Existence of small global solutions is proved in spaces with the right homogeneity to allow self-similar solutions. Moreover, we analyze the long time behavior of the solutions and obtain a class of asymptotically self-similar ones.