On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime

2019 ◽  
Vol 397 ◽  
pp. 108838 ◽  
Author(s):  
Jingwei Hu ◽  
Shi Jin ◽  
Ruiwen Shu
Keyword(s):  
Boltzmann Equation ◽  
Galerkin Approximation ◽  
Fluid Regime ◽  
Nonlinear Boltzmann Equation ◽  
Stochastic Galerkin

scholarly journals On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation

2021 ◽  
Author(s):  
Shi Jin ◽  
Esther Daus ◽  
Liu Liu
Keyword(s):  
Boltzmann Equation ◽  
Galerkin Approximation ◽  
Single Species ◽  
Collision Kernel ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time ◽  
Stochastic Galerkin ◽  
Analytical Tools ◽  
Gap Estimate

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, 1367–1443, 2016] for the deterministic problem in the perturbative regime, and in [E. S. Daus, S. Jin and L. Liu, Kinet. Relat. Models, 12, 909–922, 2019] for the single-species problem with uncertainty. The well-posedness result of the sensitivity system presented here has not been obtained so far even for the single-species case.

The solution of nonlinear Boltzmann equation with an external force

2001 ◽  
Vol 12 (8) ◽  
pp. 1385-1391 ◽  
Author(s):  
S.A. El-Wakil ◽  
A. Elhanbaly ◽  
A. Elgarayhi
Keyword(s):  
Boltzmann Equation ◽  
External Force ◽  
Nonlinear Boltzmann Equation
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