Exponential stability of the solutions of the Boltzmann equation for the Benard problem

Anne Nouri (1) , R. Esposito (2) , Leif Arkeryd (3) , Marra Rossana (4)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 MEMOCS - International Research Center for the Mathematics & Mechanics of Complex Systems
3 Chalmers University of Technology [Göteborg]
4 INFN, Sezione di Roma Tor Vergata - Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata

We complete the result in the former paper 'Stability for Rayleigh-benard convective solutions of the Boltzmann equation' by showing the exponential decay of the perturbation of the laminar solution below the critical Rayleigh number and of the convective solutions above the critical Rayleigh number, in the kinetic framework.

Domaines: Equations aux dérivées partielles [math.AP]

Anne Nouri, R. Esposito, Leif Arkeryd, Marra Rossana. Exponential stability of the solutions of the Boltzmann equation for the Benard problem. Kinetic and Related Models , 2012, 5, pp.673-695. ⟨hal-00823906⟩