We consider the Cauchy problem for the incompressible Navier-Stokes equations on the whole space R 3 , with initial value u 0 ∈ BMO −1 (as in Koch and Tataru's theorem) and with force f = div F with F ∈ L 1 F −1 L 1 (as in Lei and Lin's theorem). If u 0 and F are small enough, we show the existence of a global mild solution.