Stability of global equilibrium for the multi-species Boltzmann equation in $L^\infty$ settings

Marc Briant (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We prove the stability of global equilibrium in a multi-species mixture , where the different species can have different masses, on the 3-dimensional torus. We establish stability estimates in L ∞ x,v (w) where w = w(v) is either polynomial or exponential, with explicit threshold. Along the way we extend recent estimates and stability results for the mono-species Boltzmann operator not only to the multi-species case but also to more general hard potential and Maxwellian kernels.

Mots clés: Multi-species mixture; Boltzmann equation; Perturbative theory; Stability in L ∞; Exponential trend to equilibrium

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Marc Briant. Stability of global equilibrium for the multi-species Boltzmann equation in $L^\infty$ settings. Discrete and Continuous Dynamical Systems - Series A, 2016, 36 (12), pp.6669 - 6688. ⟨10.3934/dcds.2016090⟩. ⟨hal-01492053⟩