Self-similar solutions of the three dimensional Navier-Stokes equation

Details Self-similar solutions of the three dimensional Navier-Stokes equation Self-similar solutions of the three dimensional Navier-Stokes equation

2011-02-27

arxiv.org/abs/1102.5504v3

Physics

Mathematical Physics

14 pages, 5 figures the manuscript is published in the Communication in Theoretical Physics 56, (2011) 745-750

Scientific paper

In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.

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