, Volume 163, Issue 2, pp 415-431

Kinetic formulation of the isentropic gas dynamics andp-systems

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Abstract

We consider the 2×2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called thep-system). We show that they can be reformulated as a kinetic equation, using an additional kinetic variable. Such a formulation was first obtained by the authors in the case of multidimensional scalar conservation laws. A new phenomenon occurs here, namely that the advection velocity is now a combination of the macroscopic and kinetic velocities. Various applications are given: we recover the invariant regions, deduce newL estimates using moments lemma and proveL w* stability for γ≥3.

Communicated by J.L. Lebowitz