Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

Authors: Pierre-Emmanuel Jabin and Thomas Rey
Journal: Quart. Appl. Math. 75 (2017), 155-179
MSC (2010): Primary 35A23, 35B40, 35L67, 35L80
DOI: https://doi.org/10.1090/qam/1442
Published electronically: July 5, 2016
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Abstract: We investigate the behavior of granular gases in the limit of small Knudsen number, that is, very frequent collisions. We deal with the strongly inelastic case in one dimension of space and velocity. We are able to prove the convergence toward the pressureless Euler system. The proof relies on dispersive relations at the kinetic level, which leads to the so-called Oleinik property at the limit.

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Additional Information

Pierre-Emmanuel Jabin
Affiliation: CSCAMM and Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: pjabin@umd.edu

Thomas Rey
Affiliation: Laboratoire P. Painlevé, CNRS UMR 8524, Université Lille 1, 59655 Villeneuve d’Ascq Cedex, France
Email: thomas.rey@math.univ-lille1.fr

DOI: https://doi.org/10.1090/qam/1442
Received by editor(s): March 3, 2016
Published electronically: July 5, 2016
Additional Notes: The first author was partially supported by NSF Grant 1312142 and by NSF Grant RNMS (Ki-Net) 1107444.
The second author was partially supported by the team Inria/Rapsodi, Labex CEMPI (ANR-11-LABX-0007-01) and NSF Grant RNMS (Ki-Net) 1107444.
Article copyright: © Copyright 2016 Brown University

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