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Kinetic formulation of the isentropic gas dynamics and p-systems

Lions, Pierre-Louis; Perthame, Benoît; Tadmor, E. (1994), Kinetic formulation of the isentropic gas dynamics and p-systems, Communications in Mathematical Physics, 163, 2, p. 415-431. http://dx.doi.org/10.1007/BF02102014

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Type
Article accepté pour publication ou publié
Date
1994
Journal name
Communications in Mathematical Physics
Volume
163
Number
2
Publisher
Springer
Pages
415-431
Publication identifier
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Author(s)
Lions, Pierre-Louis
Perthame, Benoît cc
Tadmor, E.
Abstract (EN)
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 new L ∞ estimates using moments lemma and proveL ∞−w* stability for γ≥3.
Subjects / Keywords
p-system