\(L^1\) continuous dependence for the Euler equations of compressible fluids dynamics (Q1409266)

The paper deals with the entropy solutions of both the isentropic Euler equations and the full Euler equations in one space dimension. Concerning the latter, the authors prove the \(L^1\) stability of solutions sufficiently close to a constant state away from vacuum and of total variation bounded by some universal constant, assuming additionally a polytropic perfect gas law, while for the former, they prove the same result with no \(L^\infty\) smallness restriction and a general (monotone) pressure law. Their technique is a continuation of their earlier paper [Arch. Ration. Mech. Anal. 157, No. 1, 35--73 (2001; Zbl 0980.35099)].