Abstract
This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of Finn and Gilbarg (Acta Math 98:265-296, 1957); Payne and Weinberger (Acta Math 98:297-299, 1957); Dong and Ou (Commun Partial Differ Equ 18(1–2):355–379, 1993); and Liu and Yuan (Calc Var Partial Differ Equ 49(1–2):1–36, 2014). The maximum principle is applied to estimate the potential function, by choosing the proper compared functions. Then, by the weighted Schauder estimates, the convergence rates of velocity at the far field are shown as \(|{\textbf{x}}|^{-n+1}\). Furthermore, we construct the examples to show the optimality of our convergence rates and the expansion of the incompressible airfoil flow at infinity, indicating the higher convergence rates \(|{\textbf{x}}|^{-n}\).
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Acknowledgements
The research of Lei Ma was partially supported in partial by NSFC Grants 12301288. The research of Tian-Yi Wang was supported in partial by NSFC Grants 11971307 and 12061080. The authors would like to thank Professor Chunjing Xie and Professor Wen Yang for helpful discussions.
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Ma, L., Wang, TY. On the convergence rates of multi-dimensional subsonic irrotational flows in unbounded domains. Z. Angew. Math. Phys. 74, 240 (2023). https://doi.org/10.1007/s00033-023-02128-0
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DOI: https://doi.org/10.1007/s00033-023-02128-0