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

Abstract

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