Convergence of the lax-friedrichs' scheme for equations of isentropic gas dynamics in lagrangian coordinates*'

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Original languageEnglish
Pages (from-to)1441-1460
Journal / PublicationCommunications in Partial Differential Equations
Issue number8-9
Publication statusPublished - 1 Jan 1991
Externally publishedYes


By compensated compactness theory, Diperna[1,2], Ding, Chen, Luo[3] have solved the equations of elasticity and the equations of isentropic gas dynamics in Euler coordinates with a polytropic equation of state. Their framework essentially depends on the boundedness of the invariant regions of the systems. We now consider the equations of isentropic gas dynamics in Lagrangian coordinates, whose invariant regions are unbounded. Diperna showed that[1]. in order to solve the system, the major step is to find a uniform bound of the difference approximations of the Lax-Friedrichs scheme or a uniform bound of the solutions to the systems with viscous terms. However, it is still an open problem how to find the uniform bounds. © 1991, Taylor & Francis Group. All rights reserved.