Abstract
The author proved the existence of a unique solution of the Navier-Stokes equations for a viscous incompressible and compressible fluids. A method is also proposed for the search for this solution, which consists in moving along the gradient to the unique saddle point of some functional. It should be noted the complexity software implementation for its. For a viscous incompressible fluid, a simple method for finding a solution is proposed, consisting in moving along a gradient to a single point of a convex functional. An explanation is proposed for the mechanism of the appearance of turbulent flows. A method for solving the Navier-Stokes equations with turbulence is proposed. For the stationary case, experimental programs have been developed in the MATLAB system
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