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The isothermal limit for the compressible Euler equations with damping

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  • We consider the isothermal Euler system with damping. We explicitly compute the propagation and the behavior of Gaussian initial data, then we show the weak $ L^1 $ convergence of the density as well as the asymptotic behavior of its first and second moments. We also rigorously show the convergence of Barenblatt solutions towards a limit Gaussian profile in the isothermal limit $ \gamma \rightarrow 1 $.

    Mathematics Subject Classification: Primary: 76N99, 35C05; Secondary: 76Y05.


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  • Figure 1.  Convergence of $ \mathcal{B}_{\gamma} $ towards its limit Gaussian profile

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