The isothermal limit for the compressible Euler equations with damping

Quentin Chauleur

doi:10.3934/dcdsb.2022059

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2022, Volume 27, Issue 12: 7671-7687. Doi: 10.3934/dcdsb.2022059

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The isothermal limit for the compressible Euler equations with damping

Quentin Chauleur

Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France

Received: September 2021

Revised: February 2022

Early access: March 2022

Published: December 2022

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Abstract

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 $.

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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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