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Power Series for Solutions of the 3 \({\mathcal D}\)-Navier-Stokes System on R 3

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In this paper we study the Fourier transform of the \(3 \mathcal{D}\)-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 \(\Phi (\alpha , \alpha )\) of functions \(v(k ) \, = \, \frac{c(k)}{|k|^\alpha}\) where \(\alpha = 2 + \epsilon , \, \epsilon > 0\) and c (k) is bounded, \(\sup_{k \in R^3 \, \smallsetminus \, 0} \; | c ( k ) | < \infty\). 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 \(\exp \{ - {\rm const} \, \sqrt{t} | k |\}\).

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, USA

    Yakov Sinai

  2. Landau Institute of Theoretical Physics, Moscow, Russia

    Yakov Sinai

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  1. Yakov Sinai
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Correspondence to Yakov Sinai.

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Sinai, Y. Power Series for Solutions of the 3 \({\mathcal D}\)-Navier-Stokes System on R 3 . J Stat Phys 121, 779–803 (2005). https://doi.org/10.1007/s10955-005-8670-x

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  • DOI: https://doi.org/10.1007/s10955-005-8670-x

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