In this paper, we present rotational and self-similar solutions for the compressible Euler equations in R³using the separation method. These solutions partly complement Yuen’s irrotational and elliptic solutions inR³ (Yuen, 2012)  as well as rotational and radial solutions in R2 (Yuen, 2014) . 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. Copyright © 2014 Elsevier B.V.
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Early online date||Jul 2014|
|Publication status||Published - 2015|
CitationYuen, M. (2015). Rotational and self-similar solutions for the compressible Euler equations in R³. Communications in Nonlinear Science and Numerical Simulation, 20(3), 634-640.
- Compressible Euler equations
- Rotational solutions
- Self-similar solutions
- Symmetry reduction
- Navier–Stokes equations