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

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

2006-09-28

arxiv.org/abs/math/0609781v2

Mathematics

Analysis of PDEs

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

Scientific paper

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.

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