## Kinetic formulation of the isentropic gas dynamics and $$p$$-systems.(English)Zbl 0799.35151

Summary: We consider the $$2\times 2$$ 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 $$L^ \infty$$ estimates using moments lemma and prove $$L^ \infty- w*$$ stability for $$\gamma\geq 3$$.

### MSC:

 35L65 Hyperbolic conservation laws 76N15 Gas dynamics (general theory) 35B45 A priori estimates in context of PDEs

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### References:

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