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

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Abstract

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) [17] as well as rotational and radial solutions in R2 (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. Copyright © 2014 Elsevier B.V.
Original languageEnglish
Pages (from-to)634-640
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume20
Issue number3
Early online dateJul 2014
DOIs
Publication statusPublished - 2015

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Compressible Euler Equations
Radial Solutions
Self-similar Solutions
Euler equations
Computational Fluid Dynamics
Global Existence
Blow-up
Vortex
Complement
Dynamical system
Computational fluid dynamics
Dynamical systems
Vortex flow
Concretes

Citation

Yuen, 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.

Keywords

  • Compressible Euler equations
  • Rotational solutions
  • Self-similar solutions
  • Symmetry reduction
  • Vortices
  • 3-dimension
  • Navier–Stokes equations