Volume 55, Number 4, July-August 2021
|Page(s)||1323 - 1345|
|Published online||07 July 2021|
On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation*
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8—10, 1040 Wien, Austria
2 School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China
3 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR
* Corresponding author: email@example.com
Accepted: 6 May 2021
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty coming from the initial data and collision kernel is studied. Well-posedness and long-time behavior – exponential decay to the global equilibrium – of the analytical solution, and spectral gap estimate for the corresponding linearized gPC-based stochastic Galerkin system are obtained, by using and extending the analytical tools provided in [M. Briant and E.S. Daus, Arch. Ration. Mech. Anal. 3 (2016) 1367–1443] for the deterministic problem in the perturbative regime, and in [E.S. Daus, S. Jin and L. Liu, Kinet. Relat. Models 12 (2019) 909–922] for the single-species problem with uncertainty. The well-posedness result of the sensitivity system presented here has not been obtained so far neither in the single species case nor in the multi-species case.
Mathematics Subject Classification: 35Q20 / 65M70
Key words: Multi-species Boltzmann equation / uncertainty quantification / hypocoercivity / stochastic Galerkin
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.