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In fluid mechanics, a lot of authors have been executing their researches toobtain the analytical solutions of Navier-Stokes equations, even for 3D case ofcompressible gas flow or 3D case of non-stationary flow of incompressiblefluid. But there is an essential deficiency of non-stationary solutions indeed.We explore the ansatz of derivation of non-stationary solution for theNavier-Stokes equations in the case of incompressible flow, which was suggestedearlier. In general case, such a solution should be obtained from the mixedsystem of 2 Riccati ordinary differential equations (in regard to thetime-parameter t). But we find an elegant way to simplify it to the properanalytical presentation of exact solution (such a solution is exponentiallydecreasing to zero for t going to infinity). Also it has to be specified thatthe solutions that are constructed can be considered as a class of perturbationabsorbed exponentially as t going to infinity by the null solution.

A procedure for the construction of non-stationary Riccati-type flows for incompressible 3D Navier-Stokes equations