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| A Study of Hyperbolicity of Kinetic Stochastic Galerkin System for the Isentropic Euler Equations with Uncertainty |
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Citation： |
Shi JIN,Ruiwen SHU.A Study of Hyperbolicity of Kinetic Stochastic Galerkin System for the Isentropic Euler Equations with Uncertainty[J].Chinese Annals of Mathematics B,2019,40(5):765~780 |
| Page view： 517
Net amount： 389 |
Authors： |
Shi JIN; Ruiwen SHU |
Foundation： |
This work was supported by NSF Grants DMS-1522184,
DMS-1819012, DMS-1107291: RNMS KI- Net and the National Natural
Science Foundation of China (Nos.31571071, 11871297). |
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| Abstract： |
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. |
Keywords： |
Hyperbolic equations, Uncertainty quantification, Stochastic Galerkin methods |
Classification： |
35L65, 65L60 |
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