Steady Euler flows with contact discontinuities in infinitely long nozzles with general upstream data
Abstract
We investigate steady compressible Euler flows in two-dimensional infinitely long nozzles, where the piecewise smooth upstream data admit a contact discontinuity. Except for the subsonicity condition, no additional constraints are imposed on the data. We establish existence and uniqueness on the maximal interval of wall amplitudes containing the straight-nozzle configuration, and show that the contact discontinuity curve is of class C2,α. An Euler--Lagrange transformation reduces the problem to a scalar elliptic equation in divergence form on a fixed strip, with discontinuous coefficients and the contact discontinuity conditions incorporated into the weak formulation. We further investigate the downstream asymptotic behavior and show that the convergence rate of the flow matches that of the nozzle walls.
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BibTeX
@misc{chen2026steady,
title = {{Steady Euler flows with contact discontinuities in infinitely long nozzles with general upstream data}},
author = {Jun Chen and Xuemei Deng and Xiaoguang You},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.04804},
eprint = {2607.04804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04804},
}
RIS
TY - UNPB
TI - Steady Euler flows with contact discontinuities in infinitely long nozzles with general upstream data
AU - Jun Chen
AU - Xuemei Deng
AU - Xiaoguang You
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2607.04804
UR - https://arxiv.org/abs/2607.04804
AB - We investigate steady compressible Euler flows in two-dimensional infinitely long nozzles, where the piecewise smooth upstream data admit a contact discontinuity. Except for the subsonicity condition, no additional constraints are imposed on the data. We establish existence and uniqueness on the maximal interval of wall amplitudes containing the straight-nozzle configuration, and show that the contact discontinuity curve is of class C^2,α. An Euler--Lagrange transformation reduces the problem to a scalar elliptic equation in divergence form on a fixed strip, with discontinuous coefficients and the contact discontinuity conditions incorporated into the weak formulation. We further investigate the downstream asymptotic behavior and show that the convergence rate of the flow matches that of the nozzle walls.
ER -