Geodesic
Exact solution of 3d Navier--Stokes equations for potential motions of an incompressible fluid
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 1, Tome 227 (2023), pp. 41-50

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A procedure for constructing an exact solution of the 3D Navier–Stokes equations for the case of potential motion of an incompressible fluid in a deep, large-volume reservoir is proposed. The solution is considered under asymptotic boundary conditions that correspond to a given value of the velocity vector at great depth. The procedure for constructing a solution is based on the integral of the 3D Navier–Stokes equations. By introducing functions of a complex variable, the problem is reduced to a system of Riccati equations, which can be solved analytically. The qualitative features of the solution are examined.
Keywords: Navier–Stokes equations, potential motion, integral, function of a complex variable
Mots-clés : viscous fluid, Riccati equation 
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     author = {A. V. Koptev},
     title = {Exact solution of 3d {Navier--Stokes} equations for potential motions of an incompressible fluid},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {41--50},
     publisher = {mathdoc},
     volume = {227},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_227_a2/}
}
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A. V. Koptev. Exact solution of 3d Navier--Stokes equations for potential motions of an incompressible fluid. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 1, Tome 227 (2023), pp. 41-50. http://geodesic.mathdoc.fr/item/INTO_2023_227_a2/