Power series for solutions of the 3D-Navier-Stokes system on R ³

In this paper we study the Fourier transform of the 3D -Navier-Stokes System without external forcing on the whole space R ³. The properties of solutions depend very much on the space in which the system is considered. In this paper we deal with the space Φ (α , α ) of functions v(k ) = c(k)/|k|α where α = 2 + ε, ε > 0 and c (k) is bounded, sup_{k∈ R3\0}|c(k)< ∞ . We construct the power series which converges for small t and gives solutions of the system for bounded intervals of time. These solutions can be estimated at infinity (in k-space) by exp {-const√t|k|}.