Minimal $L^3$-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 (arXiv:1012.0145v2) with techniques based on profile decomposition. Our method is based on suitable splittings and energy methods. 
Hao Jia, Vladim\'ir \v{S}ver\'ak
math.AP