Preprint A690/2011
$L^\infty$ solutions for a model of non-isothermal polytropic gas flow

Kenneth Karlsen | Frid, Hermano | Holden, Helge

**Keywords: **
gas dynamics | polytropic gas | Fourier law

We establish the global existence of $L^\infty$ solutions for
a model of polytropic gas flow with varying temperature governed by a Fourier equation in the Lagrangian coordinates. The result
is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax--Friedrichs and Godunov schemes. Such convergence is achieved by proving
the estimates required for the application of the
compensated compactness theory.