Advances in Differential Equations

Stratified weak solutions of the 1-D Lagrangian Euler equations are viscosity solutions

Alexis Museux

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Recently, a class of weak solutions called "stratified" solutions have been introduced for systems of conservation laws in 1d which have a linear degenerate field and a "good symmetrizer," like the Euler system of entropic gaz dynamics ([5], [16]). These solutions can have an unbounded local variation and they generalize the "large-amplitude oscillatory solutions" previously studied by W.E, A. Heibig, and D. Serre ([13], [7], [22]). In this paper we show that, in the case of the Lagragian Euler equations of gaz dynamics, these stratified solutions are the limit of solutions of a vanishing viscosity perturbation of the system.

Article information

Adv. Differential Equations, Volume 9, Number 11-12 (2004), 1395-1436.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws
Secondary: 35B65: Smoothness and regularity of solutions 35D05 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 76N15: Gas dynamics, general


Museux, Alexis. Stratified weak solutions of the 1-D Lagrangian Euler equations are viscosity solutions. Adv. Differential Equations 9 (2004), no. 11-12, 1395--1436.

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