Large-time behavior in incompressible Navier-Stokes equations

We give a development up to the second order for strong solutions u of incompressible Naviel-Stokes equations in R(n), n greater than or equal to 2. By combining estimates obtained from the integral equation with a scaling technique, we prove that, for initial data satisfying some integrability conditions (and small enough, if n greater than or equal to 3), u behaves like the solution of the heat equation taking the same initial data as u plus a corrector term that we compute explicitely.