Abstract
In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier–Stokes equations, even for 3D case of compressible gas flow or 3D case of non-stationary flow of incompressible fluid. But there is an essential deficiency of non-stationary solutions indeed. We explore the ansatz of derivation of non-stationary solution for the Navier–Stokes equations in the case of incompressible flow, which was suggested earlier. In general case, such a solution should be obtained from the mixed system of 2 Riccati ordinary differential equations (in regard to the time-parameter t). But we find an elegant way to simplify it to the proper analytical presentation of exact solution (such a solution is exponentially decreasing to zero for t going to infinity \(\infty \)). Also it has to be specified that the solutions that are constructed can be considered as a class of perturbation absorbed exponentially as t going to infinity \(\infty \) by the null solution.
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Acknowledgments
I am thankful to unknown esteemed Reviewer for valuable comprehensive advices in preparing of this manuscript. I devote this article to my darling wife, Helen Ershkova, who is preparing for giving birth to our beloved daughter (February 2016).
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Ershkov, S.V. A procedure for the construction of non-stationary Riccati-type flows for incompressible 3D Navier–Stokes equations. Rend. Circ. Mat. Palermo 65, 73–85 (2016). https://doi.org/10.1007/s12215-015-0219-5
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DOI: https://doi.org/10.1007/s12215-015-0219-5