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.
Keywords: Multi-species Boltzmann equation, uncertainty quantification, hypocoercivity, stochastic Galerkin
@article{M2AN_2021__55_4_1323_0,
author = {Daus, Esther S. and Jin, Shi and Liu, Liu},
title = {On the multi-species {Boltzmann} equation with uncertainty and its stochastic {Galerkin} approximation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1323--1345},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {4},
doi = {10.1051/m2an/2021022},
mrnumber = {4281735},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021022/}
}
TY - JOUR AU - Daus, Esther S. AU - Jin, Shi AU - Liu, Liu TI - On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1323 EP - 1345 VL - 55 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021022/ DO - 10.1051/m2an/2021022 LA - en ID - M2AN_2021__55_4_1323_0 ER -
%0 Journal Article %A Daus, Esther S. %A Jin, Shi %A Liu, Liu %T On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1323-1345 %V 55 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021022/ %R 10.1051/m2an/2021022 %G en %F M2AN_2021__55_4_1323_0
Daus, Esther S.; Jin, Shi; Liu, Liu. On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1323-1345. doi: 10.1051/m2an/2021022
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Cité par Sources :
E.S. Daus acknowledges partial support from the Austrian Science Fund (FWF), grants P27352 and P30000, S. Jin is supported by NSFC grant No. 12031013, L. Liu is supported by the start-up fund from The Chinese University of Hong Kong.
