Open AccessThe isothermal limit for the compressible Euler equations with damping
Author(s) -
Quentin Chauleur
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series 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) , mathematics , gaussian , compressibility , euler's formula , euler equations , physics , mathematical physics , mathematical analysis , quantum mechanics , thermodynamics , 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} .