Fine properties of self-similar solutions of the Navier-Stokes equations

Details Fine properties of self-similar solutions of the Navier-Stokes equations Fine properties of self-similar solutions of the Navier-Stokes equations

2008-03-03

arxiv.org/abs/0803.0210v1

Arch. Rational Mech. Anal. 192 (2009) 375--401

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00205-008-0149-x

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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