Regularity of Solutions to the Navier-stokes Equations Evolving from Small Data in Bmo−1 Pierre Germain, Nataša Pavlović, and Gigliola Staffilani

In 2001, H. Koch and D. 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 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.