  In this paper, we present rotational and self-similar solutions for the
compressible Euler equations in R^3 using the separation method. These
solutions partly complement Yuen's irrotational and elliptic solutions in R^3
[Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 4524-4528] as well as
rotational and radial solutions in R^2 [Commun. Nonlinear Sci. Numer. Simul. 19
(2014), 2172-2180]. A newly deduced Emden dynamical system is obtained. Some
blowup phenomena and global existences of the responding solutions can be
determined. The 3D rotational solutions provide concrete reference examples for
vortices in computational fluid dynamics.
