Exact solution of 3d Navier–Stokes equations for potential motions of an incompressible fluid

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.