Regularity of solutions to the navier-stokes equations evolving from small data in BMO^-1

In 2001, Koch and Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in R^d for initial data small enough in BMO^-1.We show in this paper 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.