Supplement to "Self-similar solutions with elliptic symmetry for the compressible Euler and Navier-Stokes equations in RN" [Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 4524-4528]

Abstract 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 R N . 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 R N . 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 .

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