Fine large-time asymptotics for the axisymmetric Navier–Stokes equations

We examine the large-time behavior of axisymmetric solutions without swirl of the Navier–Stokes equation in \({\mathbb {R}}^3\) ${\mathbb{R}}^3$ . We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in the simplicity of the applied techniques: Our approach is completely based on standard \(L^2\) $L^2$ -based entropy methods.