Minimal initial data for potential Navier–Stokes singularities

Assuming some initial data u0 ∈ ˙H 1/2(R3) lead to a singularity for the 3d Navier–Stokes equations, we show that there are also initial data with the minimal ˙H 1/2-norm which will produce a singularity. © 2010 Elsevier Inc. All rights reserved.