  We consider the wellposedness of the fractional Navier-Stokes as a
generalization of the wellposedness result in Koch-Tataru's paper. An
interesting remark is that our result does not contradict to the well-known
ill-posedness result for Navier-Stokes with initial data in $\dot B^{-1,
\infty}_\infty$ by Bourgain-Pavlovic. In the end, we also discuss the
regularity and analyticity in the space variable.
