  A proof of existence, uniqueness and smoothness of the Navier-Stokes
equations is an actual problem, which solution is important for different
branches of science. The subject of this study is obtaining the smooth and
unique solutions of the three-dimension Stokes-Navier equations for the initial
and boundary value problem. The analysis shows that there exist no viscous
solutions of the Navier-Stokes equations in three dimensions. The reason is the
insufficient capability of the divergence-free velocity field. It is necessary
to modify the Navier-Stokes equations for obtaining the desirable solutions.
The modified equations describe a three-dimension flow of incompressible fluid
which sticks to a body surface. The equation solutions show the resonant blowup
of the laminar flow, laminar-turbulent transition, the fluid detachment that
opens the way to solve the magnetic dynamo problem.
