Fine properties of self-similar solutions of the Navier-Stokes equations
Résumé
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 $a(x)$.
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