Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO^{-1}

Abstract

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 $BM{O}^{-1}$. 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.

32 pages, a proof of spatial analyticity included, a regularity result for the self-similar solutions added

References in corpus (1)

• On the local Smoothness of Solutions of the Navier-Stokes Equations

Cited by in corpus (2)

• Liouville theorems for the Navier-Stokes equations and applications
• On the Analyticity of Solutions to the Navier-Stokes Equations with Fractional Dissipation