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arXiv · 2109.03590

The isothermal limit for the compressible Euler equations with damping

Quentin Chauleur
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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 $\gamma$ $\rightarrow$ 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 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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Quentin Chauleur. 2021-09-08. The isothermal limit for the compressible Euler equations with damping. https://arxiv.org/abs/2109.03590

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