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Stability of stationary solutions for the unipolar isentropic compressible Navier–Stokes–Poisson system
Author(s) -
Hong Hakho,
Kim Jinsung
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7474
Subject(s) - mathematics , isentropic process , exponential stability , perturbation (astronomy) , norm (philosophy) , inflow , a priori and a posteriori , compressibility , mathematical analysis , stability theory , outflow , uniform norm , energy method , mechanics , physics , nonlinear system , philosophy , epistemology , meteorology , political science , law , quantum mechanics
The stationary solutions to the outflow problem for unipolar isentropic Navier–Stokes–Poisson system in a half line (0, ∞ ) have recently been shown to be asymptotically stable in 13 and 26 , provided that all the L 2 norms of initial perturbations and their derivatives are small. The main purpose of this paper is to study the asymptotic stability of the stationary solutions under large initial perturbations. First, for the outflow problem, we show that the stationary solutions are asymptotically stable, provided that only the L 2 norm of initial perturbation is small. Next, for the inflow problem, we show asymptotic stability under a large initial perturbation in the H 1 norm. The main ingredient in the proofs is a careful analysis in order to control the growth induced by nonlinearities of the system in a priori estimates.