A Study of Hyperbolicity of Kinetic Stochastic Galerkin System for the Isentropic Euler Equations with Uncertainty

被引：8

作者：

Jin, Shi ^{[1
,2
]}

Shu, Ruiwen ^{[3
]}

机构：

[1] Shanghai Jiao Tong Univ, MOE LSEC, Inst Nat Sci, Sch Math Sci, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, SHL MAC, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

[3] Univ Maryland, Dept Math, 4176 Campus Dr, College Pk, MD 20742 USA

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2019年 / 40卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Hyperbolic equations; Uncertainty quantification; Stochastic Galerkin methods; PARTIAL-DIFFERENTIAL-EQUATIONS; FOKKER-PLANCK SYSTEM; UNIFORM REGULARITY; COLLOCATION METHOD; HYPOCOERCIVITY; SPACE; MODEL;

D O I：

10.1007/s11401-019-0159-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The authors study the fluid dynamic behavior of the stochastic Galerkin (SG for short) approximation to the kinetic Fokker-Planck equation with random uncertainty. While the SG system at the kinetic level is hyperbolic, its fluid dynamic limit, as the Knudsen number goes to zero and the underlying kinetic equation approaches to the uncertain isentropic Euler equations, is not necessarily hyperbolic, as will be shown in the case study fashion for various orders of the SG approximations.

引用

页码：765 / 780

页数：16

共 42 条

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