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arXiv · 1910.02739

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

Armand Bernou·Nicolas Fournier
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Abstract

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 [AG11] and [KLT13]. 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.

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Armand Bernou, Nicolas Fournier. 2019-10-07. A coupling approach for the convergence to equilibrium for a collisionless gas. https://arxiv.org/abs/1910.02739

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