Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of solutions to the Navier-Stokes equations evolving from
  small data in BMO^{-1}   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.

7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex