Geodesic
Equivalence of Navier--Stokes equation and infinite-dimensional Burgers equation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 109-120.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we prove the equivalence of the Navier–Stokes equation and the infinite-dimensional Burgers-type equation with the Laplace–Lévy operator. An explicit formula for the solution of a certain system of linear equations arising in studying the circulation of the solution of the Navier–Stokes equation is presented. 
@article{FPM_2006_12_5_a9,
     author = {M. Yu. Neklyudov},
     title = {Equivalence of {Navier--Stokes} equation and infinite-dimensional {Burgers} equation},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {109--120},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a9/}
}
TY  - JOUR
AU  - M. Yu. Neklyudov
TI  - Equivalence of Navier--Stokes equation and infinite-dimensional Burgers equation
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2006
SP  - 109
EP  - 120
VL  - 12
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a9/
LA  - ru
ID  - FPM_2006_12_5_a9
ER  - 
%0 Journal Article
%A M. Yu. Neklyudov
%T Equivalence of Navier--Stokes equation and infinite-dimensional Burgers equation
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2006
%P 109-120
%V 12
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a9/
%G ru
%F FPM_2006_12_5_a9
M. Yu. Neklyudov. Equivalence of Navier--Stokes equation and infinite-dimensional Burgers equation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 109-120. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a9/

[1] Ikeda N., Vatanabe S., Stokhasticheskie differentsialnye uravneniya i diffuzionnye protsessy, Nauka, M., 1986 | MR | Zbl

[2] Levi P., Konkretnye problemy funktsionalnogo analiza, Nauka, M., 1967 | MR

[3] Shiryaev A. N., Veroyatnost, Nauka, M., 1989 | MR

[4] Accardi L., Gibilisco P., Volovich I., “Yang–Mills gauge fields as harmonic functions for the Lévy Laplacian”, Russian J. Math. Phys., 2:2 (1994), 235–251 | MR

[5] Accardi L., Smolyanov O. G., “Semigroups and harmonic functions generated by Lévy Laplacians”, Dokl. Math., 384:3 (2002), 295–301 | MR | Zbl

[6] Kunita H., Stochastic Flows and Stochastic Differential Equations, Cambridge Stud. Adv. Math.; Vol. 24, Cambridge Univ. Press, Cambridge, 1990 | MR | Zbl

[7] Neklyudov M. Yu., “Controllable stochastic dynamical system equivalent to the Navier–Stokes equation”, Russian J. Math. Phys., 12:2 (2005), 232–240 | MR | Zbl