Based on the characteristic method, we construct a new class of perturbational solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in Rᴺ. Such solutions are more general than those obtained by Yuen [Yuen MW. Self-similar solutions with elliptic symmetry for the compressible Euler and Navier–Stokes equations in Rᴺ. Commun Nonlinear Sci Numer Simul 17 2012; 4524–8.]. The perturbational solutions may have applications in explaining the drifting phenomena of the propagation wave like Tsunamis in oceans when N=2. Copyright © 2012 Elsevier B.V. All rights reserved.
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Publication status||Published - Jun 2013|
CitationAn, H., & Yuen, M. (2013). Supplement to “self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in Rᴺ” [Commun. Nonlinear Sci. Numer. Simu. 17 (2012) 4524-4528]. Communications in Nonlinear Science and Numerical Simulation, 18(6), 1558–1561.
- Euler equations
- Navier–Stokes equations
- Characteristic method
- Perturbational solutions
- Exact solutions
- Elliptic symmetry