TY - JOUR
T1 - Power series for solutions of the 3D-Navier-Stokes system on R 3
AU - Sinai, Yakov
N1 - Funding Information:
I would like to thank C. Fefferman and V. Yakhot for many useful discussions and remarks. M.Arnold, Dong Li and unanimous referee proposed many useful corrections. I thank them and S. Friedlander, N. Pavlovic and E. Siggia for their interest in this work. My deep gratitude goes to G. Pecht for her excellent typing of the manuscript. The financial support from NSF, Grant DMS-0245397 is highly appreciated.
PY - 2005/12
Y1 - 2005/12
N2 - 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|}.
AB - 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|}.
KW - Fourier transform
KW - Navier-Stokes System
KW - Power series
UR - http://www.scopus.com/inward/record.url?scp=29044442687&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=29044442687&partnerID=8YFLogxK
U2 - 10.1007/s10955-005-8670-x
DO - 10.1007/s10955-005-8670-x
M3 - Article
AN - SCOPUS:29044442687
SN - 0022-4715
VL - 121
SP - 779
EP - 803
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 5-6
ER -