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Regularity of
velocity averages for transport equations on random discrete
velocity grids
Nathalie Ayi and Thierry Goudon |
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Vol. 10 (2017), No. 5, 1201–1225
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Abstract |
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We go back to the question of the regularity of the “velocity average” when and both belong to , and the variable lies in a discrete subset of . First of all, we provide a rate, depending on the number of velocities, for the defect of regularity which is reached when ranges over a continuous set. Second of all, we show that the regularity holds in expectation when the set of velocities is chosen randomly. We apply this statement to investigate the consistency with the diffusion asymptotics of a Monte Carlo-like discrete velocity model. |
Keywords
average lemma, discrete velocity models, random velocity
grids, hydrodynamic limits
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Mathematical Subject Classification 2010
Primary: 35B65
Secondary: 35F05, 35Q20, 82C40
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Milestones
Received: 7 November 2016
Revised: 12 February 2017
Accepted: 28 March 2017
Published: 1 July 2017
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Authors |
| Nathalie Ayi | |
| Inria Rennes-Bretagne Atlantique,
IPSO Research team IRMAR, UMR CNRS 6625 Campus de Beaulieu Bâtiment 22/23 263 Avenue du Général Leclerc 35042 Rennes France |
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| Thierry Goudon | |
| Université Côte d’Azur, Inria, CNRS,
LJAD Parc Valrose 06108 Nice France |
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