Rotational and self-similar solutions for the compressible Euler equations in R3

Abstract 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 (Yuen, 2012) [17] as well as rotational and radial solutions in R 2 (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.

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