Communications in Mathematical Physics

, Volume 163, Issue 2, pp 415–431

Kinetic formulation of the isentropic gas dynamics andp-systems

  • P. L. Lions
  • B. Perthame
  • E. Tadmor

DOI: 10.1007/BF02102014

Cite this article as:
Lions, P.L., Perthame, B. & Tadmor, E. Commun.Math. Phys. (1994) 163: 415. doi:10.1007/BF02102014


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 proveLw* stability for γ≥3.

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • P. L. Lions
    • 1
  • B. Perthame
    • 2
  • E. Tadmor
    • 3
  1. 1.Ceremade, Université Paris IX-DauphineParis Cedex 16France
  2. 2.Laboratoire d'Analyse NumériqueUniversité P. et M. Curie T55/65Paris Cédex 05France
  3. 3.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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