Global Mild Solutions of Fractional Naiver-Stokes Equations with Small   Initial Data in Critical Besov-Q Spaces
  In this paper, we establish the global existence and uniqueness of a mild solution of the so-called fractional Navier-Stokes equations with a small initial data in the critical Besov-Q space covering many already known function spaces. 
Pengtao Li and Jie Xiao and Qixiang Yang
math.AP