Work

Time-Asymptotic Behavior of the Boltzmann Equation with Random Inputs in Whole Space and its Stochastic Galerkin Approximation

Year: 2026

Type: article

Abstract: . We consider the Boltzmann equation with random uncertainties arising from the initial data and collision kernel in the whole space, along with its stochastic Galerkin (SG) approximations. By employing Green’s function method, we show that the higher-order derivatives of the solution with respect to the random variable exhibit polynomial decay over time. These results are then applied to analyze the SG method for the SG system and to demonstrate the polynomial decay of the numerical error over time.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/25m177521x

Authors: Shi Jin, Qi Shao, Haitao Wang

Institution: Shanghai Jiao Tong University

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G2867246131, G3942283580, G7627071985