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]

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.