Self-similar solutions of the three dimensional Navier-Stokes equation
Mathematical Physics
2015-03-19 v3 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1102.5504,
title = {Self-similar solutions of the three dimensional Navier-Stokes equation},
author = {I. F. Barna},
journal= {arXiv preprint arXiv:1102.5504},
year = {2015}
}
Comments
14 pages, 5 figures the manuscript is published in the Communication in Theoretical Physics 56, (2011) 745-750