Hong, John M.; Hsu, Cheng-Hsiung; Lin, Ying-Chieh; Liu, Weishi Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area. (English) Zbl 1319.35191 J. Differ. Equations 254, No. 4, 1957-1976 (2013). This paper studies the linear stability of the sub-to super inviscid transonic stationary wave of a one-dimensional model of isentropic compressible flows through a nozzle of varying area. By using the geometric singular perturbation approach, the authors show that the sub-to super inviscid transonic stationary wave is physically relevant in the sense that it is \(L^ \infty\) linearly stable on any bounded space interval under some assumption on velocity. Reviewer: Cheng He (Beijing) Cited in 3 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76H05 Transonic flows 35B35 Stability in context of PDEs 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 76N15 Gas dynamics (general theory) Keywords:geometric singular perturbation theory; sub-to super inviscid transonic stationary wave; Sobolev’s embedding theorem PDFBibTeX XMLCite \textit{J. M. Hong} et al., J. Differ. Equations 254, No. 4, 1957--1976 (2013; Zbl 1319.35191) Full Text: DOI