Analytical solution of the steady Navier-Stokes equation for a fluid entrained by a rotating disk of finite radius using the apparatus of tunnel mathematics.

As is known, if the nonlinear terms in the Navier-Stokes equations for a viscous fluid do not vanish identically then the solution of these equations presents great difficulties, and exact solutions can be obtained only in a very small number of cases. Concerning unsteady Navier-Stokes equation, T. Tao in his article showed that it can have solutions which turn out infinite during finite time (blowup solutions).[1] And if even finite solutions exist they are presented in view of infinite series, that is inconvenient for use in practice. That`s why it is reasonable to seek solutions of steady Navier-Stokes equation in view of elementary functions. Such possibility the equations of analyticity of functions of the spatial complex variable (shortly, the equations of tunnel mathematics) represent since all vector fields, including those obeying the Navier-Stokes equation, satisfy to them. The Navier-Stokes equations themselves are then applied for verification of obtained solutions and calculation the pressure.