Stochastic discrete velocity averaging lemmas and Rosseland approximation
Nathalie Ayi1
1 IRMAR Campus de Beaulieu - Bâtiment 22/23 263 Avenue du Général Leclerc 35042 Rennes Cedex France
Séminaire Laurent Schwartz — EDP et applications (2016-2017), Talk no. 10, 10 p.

In this note, we investigate some questions around velocity averaging lemmas, a class of results which ensure the regularity of the “velocity average” ∫f(x,v)ψ(v)dμ(v) when f and v·∇ x f both belong to L p , p∈[1,∞) and the measured set of velocities (𝒱,dμ) satisfy a nondegeneracy assumption. We are interested in the case when the variable v lies in a discrete subset of ℝ D .

We present results obtained in collaboration with T. Goudon in [2]. First of all, we provide a rate, depending on the number of velocities, to the defect of H 1/2 regularity which is reached when v ranges over a continuous set. Second of all, we show that the H 1/2 regularity holds in expectation when the set of velocities is chosen randomly. We apply this statement to obtain a consistency result for the diffusion limit in the case of the Rosseland approximation.

Published online:
DOI: 10.5802/slsedp.100
Nathalie Ayi 1

1 IRMAR Campus de Beaulieu - Bâtiment 22/23 263 Avenue du Général Leclerc 35042 Rennes Cedex France 
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Nathalie Ayi. Stochastic discrete velocity averaging lemmas and Rosseland approximation. Séminaire Laurent Schwartz — EDP et applications (2016-2017), Talk no. 10, 10 p. doi : 10.5802/slsedp.100. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.100/

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