Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in RN

In this paper, we present a unified formulae for explicit self-similar solutions of the Euler/Navier-Stokes-Korteweg equations arising in the modeling of capillary fluids. The technique used here is to reduce Euler/Navier-Stokes-Korteweg equations into a series of solvable ordinary differential equations by making use of multi-dimensional self-similar ansatz and variable separation method.