The space $B^{-1}_{\infty, \infty}$, volumetric sparseness, and 3D NSE
  In the context of the $L^\infty$-theory of the 3D NSE, it is shown that suitable smallness of a solution in Besov space $B^{-1}_{\infty, \infty}$ suffices to prevent a possible blow-up. 
Aseel Farhat, Zoran Grujic and Keith Leitmeyer
math.AP