Regularity of Solutions to the Navier-Stokes Equations Evolving from Small Data in BMO−1

Abstract

In 2001, Koch and Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in ℝd for initial data small enough in <it>BMO</it>−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.