Radial Transonic Shock Solutions to Euler-Poisson System with Varying Background Charge in an Annulus
Year: 2023
Author: Ben Duan, Zhen Luo, Yuanyuan Xing
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 1 : pp. 129–156
Abstract
This paper concerns both the structural and dynamical stabilities of radially symmetric transonic shock solutions for two-dimensional Euler-Poisson system in an annulus. The density of fixed, positively charged background ions is allowed to be different constants in supersonic and subsonic regimes. First, the existence and structural stability of a steady transonic shock solution are obtained by the monotonicity between the shock location and the density on the outer circle. Second, any radially symmetric transonic shock solution with respect to small perturbations of the initial data is shown to be dynamically stable. The proof relies on the decay estimates and coupled effects from electric field and geometry of the annulus, together with the methods from [18]. These results generalize previous stability results on transonic shock solutions for constant background charge.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2022-0007
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 1 : pp. 129–156
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Euler-Poisson equations radial symmetry transonic shock varying background charge stability.