Compressible subsonic jet flows with unprescribed detachment

Jianfeng Cheng; Xiaohui Wang; Wei Xiang

doi:10.1016/j.jde.2025.114042

Compressible subsonic jet flows with unprescribed detachment

Jianfeng Cheng
, Xiaohui Wang
, Wei Xiang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

This paper is concerned with the well-posedness of the compressible subsonic jet flows issuing from a semi-infinitely long nozzle, the free streamline detaches smoothly from the nozzle wall, and the detachment is not known a priori. More specifically, given a semi-infinitely long de Laval type nozzle and an atmosphere pressure p_atm > 0, there exists a critical value m_cr > 0 and an interval [p_{_}, p¯], such that for any incoming mass flux m₀ ∈ (0, m_cr) and the pressure difference p_dif ∈ [p_{_}, p¯], there exists a unique compressible subsonic jet flow and the detachment lies on the divergent part of the nozzle wall. Moreover, the detachment is continuous and strictly monotonic with respect to p_dif. Finally, we also establish the optimal C^1, ½ -regularity of the free boundary at the detachment. © 2025 Elsevier Inc.

Original language	English
Article number	114042
Number of pages	58
Journal	Journal of Differential Equations
Volume	459
Online published	22 Dec 2025
DOIs	https://doi.org/10.1016/j.jde.2025.114042
Publication status	Published - 5 Apr 2026

Funding

Cheng is partially supported by National Key R&D Program of China (No. 2022YFA1007700) and National Natural Science Foundation of China (No. 12371237 and No. 12526202). Wang is partially supported by Natural Science Foundation of Sichuan Province Grant (No. 2025ZNSFSC0070). Xiang is partially supported by the Research Grants Council of the HKSAR, China projects (No. CityU 11304820, No. CityU 11300021, No. CityU 11311722, No. CityU 11305523, and No. CityU 11305625), by the Hong Kong Polytechnic University internal grant (No. P0045335), and in part by the Research Center for Nonlinear Analysis of the Hong Kong Polytechnic University.

Research Keywords

Existence
Uniqueness
Subsonic jet flows
Free boundary

RGC Funding Information

RGC-funded

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@article{0ebe3db7bb8e4ad2863941aaa341e162,

title = "Compressible subsonic jet flows with unprescribed detachment",

abstract = "This paper is concerned with the well-posedness of the compressible subsonic jet flows issuing from a semi-infinitely long nozzle, the free streamline detaches smoothly from the nozzle wall, and the detachment is not known a priori. More specifically, given a semi-infinitely long de Laval type nozzle and an atmosphere pressure patm > 0, there exists a critical value mcr > 0 and an interval [p\_, p¯], such that for any incoming mass flux m0 ∈ (0, mcr) and the pressure difference pdif ∈ [p\_, p¯], there exists a unique compressible subsonic jet flow and the detachment lies on the divergent part of the nozzle wall. Moreover, the detachment is continuous and strictly monotonic with respect to pdif. Finally, we also establish the optimal C1, ½ -regularity of the free boundary at the detachment. {\textcopyright} 2025 Elsevier Inc.",

keywords = "Existence, Uniqueness, Subsonic jet flows, Free boundary",

author = "Jianfeng Cheng and Xiaohui Wang and Wei Xiang",

year = "2026",

month = apr,

day = "5",

doi = "10.1016/j.jde.2025.114042",

language = "English",

volume = "459",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Compressible subsonic jet flows with unprescribed detachment

AU - Cheng, Jianfeng

AU - Wang, Xiaohui

AU - Xiang, Wei

PY - 2026/4/5

Y1 - 2026/4/5

N2 - This paper is concerned with the well-posedness of the compressible subsonic jet flows issuing from a semi-infinitely long nozzle, the free streamline detaches smoothly from the nozzle wall, and the detachment is not known a priori. More specifically, given a semi-infinitely long de Laval type nozzle and an atmosphere pressure patm > 0, there exists a critical value mcr > 0 and an interval [p_, p¯], such that for any incoming mass flux m0 ∈ (0, mcr) and the pressure difference pdif ∈ [p_, p¯], there exists a unique compressible subsonic jet flow and the detachment lies on the divergent part of the nozzle wall. Moreover, the detachment is continuous and strictly monotonic with respect to pdif. Finally, we also establish the optimal C1, ½ -regularity of the free boundary at the detachment. © 2025 Elsevier Inc.

AB - This paper is concerned with the well-posedness of the compressible subsonic jet flows issuing from a semi-infinitely long nozzle, the free streamline detaches smoothly from the nozzle wall, and the detachment is not known a priori. More specifically, given a semi-infinitely long de Laval type nozzle and an atmosphere pressure patm > 0, there exists a critical value mcr > 0 and an interval [p_, p¯], such that for any incoming mass flux m0 ∈ (0, mcr) and the pressure difference pdif ∈ [p_, p¯], there exists a unique compressible subsonic jet flow and the detachment lies on the divergent part of the nozzle wall. Moreover, the detachment is continuous and strictly monotonic with respect to pdif. Finally, we also establish the optimal C1, ½ -regularity of the free boundary at the detachment. © 2025 Elsevier Inc.

KW - Existence

KW - Uniqueness

KW - Subsonic jet flows

KW - Free boundary

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001650430400002

U2 - 10.1016/j.jde.2025.114042

DO - 10.1016/j.jde.2025.114042

M3 - RGC 21 - Publication in refereed journal

SN - 0022-0396

VL - 459

JO - Journal of Differential Equations

JF - Journal of Differential Equations

M1 - 114042

ER -

Compressible subsonic jet flows with unprescribed detachment

Abstract

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Research Keywords

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GRF: Determining Free Boundary in a Nozzle for Compressible Euler Flow

GRF: Multi-Dimensional Steady Contact Discontinuity

GRF: Persistence of Steady Structures under Unsteady Perturbations

Cite this

Compressible subsonic jet flows with unprescribed detachment

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Determining Free Boundary in a Nozzle for Compressible Euler Flow

GRF: Multi-Dimensional Steady Contact Discontinuity

GRF: Persistence of Steady Structures under Unsteady Perturbations

Cite this