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- Title
- Transonic shocks for three-dimensional axisymmetric flows in divergent nozzles
- KIAS Author
- Park, Hyangdong
- Journal
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025
- Archive
-
- Abstract
- We prove the stability of three-dimensional axisymmetric solutions to the steady Euler system with transonic shocks in divergent nozzles under perturbations of the exit pressure and the supersonic solution in the upstream region. We first derive a free boundary problem with the newly introduced formulation of the Euler system for three-dimensional axisymmetric flows in divergent nozzles via the method of Helmholtz decomposition. We then construct an iteration scheme and use the Schauder fixed point theorem and weak implicit function theorem to solve the problem. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.