The isothermal limit for the compressible Euler equations with damping | Zendy

Quentin Chauleur | Zendy

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The isothermal limit for the compressible Euler equations with damping

Author(s) -

Quentin Chauleur

Publication year - 2022

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2022059

Subject(s) - limit (mathematics) , isothermal process , convergence (economics) , compressibility , euler equations , mathematics , gaussian , physics , euler's formula , mathematical physics , mathematical analysis , thermodynamics , quantum mechanics , economics , economic growth

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 \begin{document}$ L^1 $\end{document} convergence of the density as well as the asymptotic behavior of its first and second moments. We also rigorously show the convergence of Barenblatt solutions towards a limit Gaussian profile in the isothermal limit \begin{document}$ \gamma \rightarrow 1 $\end{document} .

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