Isentropic Approximation¶of the Compressible Euler System¶in One Space Dimension

Abstract:

Using the stability results of Bressan & Colombo [BC] for strictly hyperbolic 2 × 2 systems in one space dimension, we prove that the solutions of isentropic and non-isentropic Euler equations in one space dimension with the respective initial data (ρ₀, u ₀) and (ρ₀, u ₀, &\theta;₀=ρ₀ ^{γ− 1}) remain close as soon as the total variation of (ρ₀, u ₀) is sufficiently small.