Communications in Mathematical Sciences

Volume 19 (2021)

Number 5

Global discontinuous solution for $1D$ isentropic gas dynamics system

Pages: 1451 – 1459

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n5.a14

Authors

Ahmad El Hajj (Université de Technologie de Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne (LMAC), Compiègne, France)

Hassan Ibrahim (Université Libanaise, Ecole Doctorale en Sciences et Technologie (EDST), Hadath, Beyrouth, Lebanon)

Vivian Rizik (Université Libanaise, EDST, Hadath, Beyrouth, Lebanon)

Abstract

In this work, we study the global existence of one-dimensional isentropic gas dynamics system. We prove a global-in-time existence result of this system in the framework of discontinuous non-decreasing solutions considering bounded initial data. We remark that this result allows us to give a global meaning to the gas dynamics system in distributional sense, considering discontinuous solutions with vacuum.

Keywords

isentropic gas dynamics system, Euler equations, non-decreasing solutions, discontinuous solutions, viscosity solutions

2010 Mathematics Subject Classification

35A01, 35D40, 35F20, 35L40, 35Q31, 74G25

Received 17 February 2020

Accepted 15 March 2021

Published 7 July 2021