  We study the solutions of the nonstationary incompressible Navier--Stokes
equations in $\R^d$, $d\ge2$, of self-similar form $u(x,t)=\frac{1}{\sqrt
t}U\bigl(\frac{x}{\sqrt t}\bigr)$, obtained from small and homogeneous initial
data $a(x)$. We construct an explicit asymptotic formula relating the
self-similar profile $U(x)$ of the velocity field to its corresponding initial
datum $a(x)$.
