On two-dimensional navier-stokes flows with rotational symmetries

Navier-Stokes flows are found on R-2 that decay in time more rapidly than observed in general. The decay rate is determined in accordance with the order of symmetry with respect to the action of dihedral groups of orthogonal transformations. Contrary to the previous work [13], the basic existence result is proved with no restriction on the size of initial data. Our result extends that of [3] under different assumptions on the initial data. Unlike [3], the proofs are all carried out without using estimates for the associated vorticity transport equations.