KINETIC FORMULATION OF THE ISENTROPIC GAS-DYNAMICS AND P-SYSTEMS

We consider the 2 x 2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called the p-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 new L(infinity) estimates using moments lemma and prove L(infinity) - w* stability for gamma greater-than-or-equal-to 3.