A coupling approach for the convergence to equilibrium for a collisionless gas

Armand Bernou (1) , Nicolas Fournier (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in Aoki and Golse, 2011 and Kuo, Liu and Tsai, 2013. This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension equal to or larger than 2 that does not require any symmetry of the domain, nor a monokinetic regime. Our study is also more general in terms of reflection at the boundary: we allow for rather general diffusive reflections and for a specular reflection component.

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

Armand Bernou, Nicolas Fournier. A coupling approach for the convergence to equilibrium for a collisionless gas. The Annals of Applied Probability, 2022, 32, pp.764--811. ⟨hal-02306374⟩