Exact Solution to the Compressible Euler System in 1-$D^∗$

Abstract

In this paper, the exact solution of one-dimensional isentropic Euler equations is studied. When the exponent of the state equation satisfies $\gamma = 2,$ we get an exact solution which is linear with respect to the spatial variable $x.$ For this end, we solve some ordinary differential equations with time dependent variable coefficients.