Minimal L³-initial data for potential navier-stokes singularities

We give a simple proof of the existence of initial data with minimal L ³-norm for potential Navier-Stokes singularities, recently established in [I. Gallagher, G. S. Koch, and F. Planchon, Math. Ann., 355 (2013), pp. 1527-1559] with techniques based on profile decomposition. Our proof is more elementary and is based on suitable splittings of initial data and energy methods. The main difficulty in the L³ case is the lack of compactness of the embedding L³ loc → L2 loc.