The isothermal limit for the compressible Euler equations with damping

We consider the isothermal Euler system with damping. We rigorously show the convergence of Barenblatt solutions towards a limit Gaussian profile in the isothermal limit $gamma$ $rightarrow$ 1, and we explicitly compute the propagation and the behavior of Gaussian initial data. We then show the weak L 1 convergence of the density as well as the asymptotic behavior of its first and second moments. Contents 1. Introduction 1 2. Assumptions and main results 3 3. The limit $gamma$ $rightarrow$ 1 of Barenblatts solutions 6 4. Gaussian solutions 9 5. Evolution of certain quantities 10 6. Convergence 15 7. Conclusion 17 References 17