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Journal Articles Discrete and Continuous Dynamical Systems - Series B Year : 2022

The isothermal limit for the compressible Euler equations with damping

Abstract

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 γ → 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 γ → 1 of Barenblatt's solutions 6 4. Gaussian solutions 9 5. Evolution of certain quantities 10 6. Convergence 15 7. Conclusion 17 References 17
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Dates and versions

hal-03335294 , version 1 (06-09-2021)
hal-03335294 , version 2 (08-09-2021)

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Quentin Chauleur. The isothermal limit for the compressible Euler equations with damping. Discrete and Continuous Dynamical Systems - Series B, 2022, ⟨10.3934/dcdsb.2022059⟩. ⟨hal-03335294v2⟩
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