Geodesic
Equivalence of Navier–Stokes equation and infinite-dimensional Burgers equation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 109-120
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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. 
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     author = {M. Yu. Neklyudov},
     title = {Equivalence of {Navier{\textendash}Stokes} equation and infinite-dimensional {Burgers} equation},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a9/}
}
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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