Well-posedness and regularity for the fractional Navier-Stokes equations

Abstract

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 ${\dot{B}}_{\infty }^{-1,\infty }$ by Bourgain-Pavlovic. In the end, we also discuss the regularity and analyticity in the space variable.

18 pages