L∞ Stability for Weak Solutions of the Navier-Stokes Equations in R3 with Singular Initial Data in Morrey Spaces

In this paper we study the L∞ stability of weak solutions of the Navier-Stokes equations when the initial data is a measure belonging to a suitable Morrey space. It is also assumed that these measures are sufficiently small in the corresponding norms. The physically relevant cases of vortex filament, vortex ring and vortex sheet structure of vorticity are included in this analysis.