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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
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 11 November 2021