Two proofs of Haff's law for dissipative gases: the use of entropy and the weakly inelastic regime

Ricardo J. Alonso (1) , Bertrand Lods (2)

1 Department of Computational and Applied Mathematics [Houston]
2 Department of Statistics and Economics

We revisit our recent contribution (SIAM J. Math. Analysis, 42 (2010) 2499--2538) and give two simpler proofs of the so-called Haff's law for granular gases (with non-necessarily constant restitution coefficient). The first proof is based upon the use of entropy and asserts that Haff's law holds whenever the initial datum is of finite entropy. The second proof uses only the moments of the solutions and holds in some weakly inelasticity regime which has to be clearly defined whenever the restitution coefficient is non-constant

Mots clés: Boltzmann equation; inelastic hard spheres; granular gas; cooling rate; Haff's law

Domaines: Equations aux dérivées partielles [math.AP]

Ricardo J. Alonso, Bertrand Lods. Two proofs of Haff's law for dissipative gases: the use of entropy and the weakly inelastic regime. 2011. ⟨hal-00588716⟩