A new proof for Koch and Tataru's result on the well-posedness of Navier-Stokes equations in $BM{O}^{-1}$

We give a new proof of a well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in ${\mathbb{R}}^n$ with small initial data in $BM{O}^{-1}({\mathbb{R}}^n)$. The proof is formulated operator theoretically and does not make use of self-adjointness of the Laplacian.