Power Series for Solutions of the 3$$-Navier-Stokes System on R3


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Abstract

In this paper we study the Fourier transform of the 3$$-Navier-Stokes System without external forcing on the whole space R3. The properties of solutions depend very much on the space in which the system is considered. In this paper we deal with the space of functions Ψ (α, α) of functions υ(k) = $$ where α= 2+∈,∈> 0 and c(k) is bounded, sup κ∈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|}

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