Rotational and self-similar solutions for the compressible Euler equations in R3R3

• We present rotational and self-similar solutions for Euler equations in R3.
• The solutions complement Yuen’s irrotational ones in R3 and rotational ones in R2.
• A newly deduced Emden dynamical system is obtained.
• Some blowup phenomena and global existences can be determined.
• The 3D rotational solutions provide concrete reference examples for vortices.

In this paper, we present rotational and self-similar solutions for the compressible Euler equations in R3R3 using the separation method. These solutions partly complement Yuen’s irrotational and elliptic solutions in R3R3 (Yuen, 2012) [17] as well as rotational and radial solutions in R2R2 (Yuen, 2014) [18]. 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.