Power Series for Solutions of the 3 ${mathcal D}$ -Navier-Stokes System on R 3
Abstract
In this paper we study the Fourier transform of the 3 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 Φ (α , α ) of functions v(k ) = c(k)/|k|^α where α = 2 + ɛ , ɛ > 0 and c ( k) is bounded, sup_{k in R^3 setminus 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 \{ - const sqrt{t} | k |\}.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- December 2005
- DOI:
- 10.1007/s10955-005-8670-x
- Bibcode:
- 2005JSP...121..779S
- Keywords:
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- Navier-Stokes System;
- Fourier transform;
- power series