The new analytical solution of the 3D Navier-Stokes equation for compressible medium clarifies the sixth Millennium Prize problem

The limitations of capabilities of the existing mathematical weather prediction (including forecasting for weather-sensitive individuals) cannot be duly realized nowadays due to the fact that till now there is no proof of the existence and uniqueness of smooth solutions of the three-dimensional (3D) Navier-Stokes equation (in any finite period of time). We have obtained a new analytical solution of the Cauchy problem of this equation in an unbounded space, which has finite energy for any values of time.