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

Yakov Sinai

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19 Scopus citations


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, supk∈ 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|}.

Original languageEnglish (US)
Pages (from-to)779-803
Number of pages25
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Dec 2005

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Fourier transform
  • Navier-Stokes System
  • Power series


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