Radial Transonic Shock Solutions to Euler-Poisson System with Varying Background Charge in an Annulus (CSIAM Transactions on Applied Mathematics, 2023)
This paper concerns both the structural and dynamical stabilities of radiallysymmetric transonic shock solutions for two-dimensional Euler-Poisson system in anannulus. The density of fixed, positively charged background ions is allowed to be different constants in supersonic and subsonic regimes. First, the existence and structuralstability of a steady transonic shock solution are obtained by the monotonicity betweenthe shock location and the density on the outer circle. Second, any radially symmetrictransonic shock solution with respect to small perturbations of the initial data is shownto be dynamically stable. The proof relies on the decay estimates and coupled effectsfrom 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.
Keywords: Euler-Poisson equations; radial symmetry; transonic shock; varying background charge; stability.