Regularity of solutions to the Navier-Stokes equations evolving from   small data in BMO^{-1}
  In 2001, H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in ${\mathbb{R}}^d$ for initial data small enough in $BMO^{-1}$. We show in this article that the Koch and Tataru solution has higher regularity. As a consequence, we get a decay estimate in time for any space derivative, and space analyticity of the solution. Also as an application of our regularity theorem, we prove a regularity result for self-similar solutions. 
Pierre Germain, Nata\v{s}a Pavlovi\'c, Gigliola Staffilani