Continuous sonic-supersonic flows in two-dimensional infinitely long divergent nozzles
Abstract
This paper concerns continuous sonic-supersonic flows in a two-dimensional infinitely long divergent nozzle with straight solid walls. For a given inlet that is a small perturbation of an arc centered at the vertex of the nozzle, we establish the global existence and uniqueness of a continuous sonic-supersonic potential flow which is close to the radially symmetric sonic-supersonic flow. The flow is sonic at the inlet, with its velocity along the normal direction, and becomes supersonic in the nozzle. Such a sonic-supersonic model is governed by a quasilinear nonstrictly hyperbolic equation with degeneracy at the inlet, and the degeneracy is weak in the sense that there exist exactly two distinct characteristics from each sonic point, except for those at the walls, pointing into the supersonic region. One of the crucial ingredients of the analysis is to obtain the precise asymptotic behavior near the sonic inlet by the method of characteristics, which is essential for establishing the local existence of continuous sonic-supersonic flows. Another one is to extend the local solution globally and derive uniform estimates in the supersonic region.
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BibTeX
@misc{qian2026continuous,
title = {{Continuous sonic-supersonic flows in two-dimensional infinitely long divergent nozzles}},
author = {Lili Qian and Chunpeng Wang and Zihao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.23415},
eprint = {2609.23415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23415},
}
RIS
TY - UNPB
TI - Continuous sonic-supersonic flows in two-dimensional infinitely long divergent nozzles
AU - Lili Qian
AU - Chunpeng Wang
AU - Zihao Zhang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.23415
UR - https://arxiv.org/abs/2609.23415
AB - This paper concerns continuous sonic-supersonic flows in a two-dimensional infinitely long divergent nozzle with straight solid walls. For a given inlet that is a small perturbation of an arc centered at the vertex of the nozzle, we establish the global existence and uniqueness of a continuous sonic-supersonic potential flow which is close to the radially symmetric sonic-supersonic flow. The flow is sonic at the inlet, with its velocity along the normal direction, and becomes supersonic in the nozzle. Such a sonic-supersonic model is governed by a quasilinear nonstrictly hyperbolic equation with degeneracy at the inlet, and the degeneracy is weak in the sense that there exist exactly two distinct characteristics from each sonic point, except for those at the walls, pointing into the supersonic region. One of the crucial ingredients of the analysis is to obtain the precise asymptotic behavior near the sonic inlet by the method of characteristics, which is essential for establishing the local existence of continuous sonic-supersonic flows. Another one is to extend the local solution globally and derive uniform estimates in the supersonic region.
ER -