Non-stationary creeping flows for incompressible 3D Navier-Stokes equations

We explore the ansatz of derivation of non-stationary creeping flows for the Navier Stokes equations in the case of incompressible flow of Newtonian fluids. In general case, such a solution should be obtained from the mixed system of 2 Riccati ordinary differential equations (in regard to time-parameter t). But we have found an elegant way to simplify it to the proper analytical presentation of creeping flow as a solution of only one Riccati ordinary differential equation, which nevertheless has no analytical solution in general case. It was a motivation to obtain the elegant approximate solution for creeping flow: - curl-free velocity field consists of the constant component U in Ox-direction, non-stationary (but negligible) component V in Oy-direction, the constant (but negligible) component W in Oz-direction. Additional component of flow velocity field (with variable curl) consists of the appropriate harmonic functions, not depending on time-parameter t. Also the suggested ansatz is illuminated by showing (on the example of creeping flow past a sphere) how it can be used to find specific solutions of current technical interest, or that it can be used to some significant advantage over some of the many existing analytical, semi-analytical, and/or numerical techniques for solution of creeping flows. (C) 2016 Elsevier Masson SAS. All rights reserved.