Space-time decay of Navier-Stokes flows invariant under rotations

Abstract

We show that the solutions to the non-stationary Navier-Stokes equations in $R^d$, $d=2,3$ which are left invariant under the action of discrete subgroups of the orthogonal group $O(d)$ decay much faster as $|x|\to\infty$ or $ t \to\infty$ than in the generic case and we compute, for each subgroup, the precise decay rates in space-time of the velocity field.