  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.
