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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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/

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