Kinetic formulation of the isentropic gas dynamics andp-systems
- Cite this article as:
- Lions, P.L., Perthame, B. & Tadmor, E. Commun.Math. Phys. (1994) 163: 415. doi:10.1007/BF02102014
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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.