@article{Wang2026, 
author = {Peikang Wang and Xuemei Deng and Min Wang},
title = {Gravitational effect on transonic shocks in finite divergent nozzle},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {7},
pages = {5087-5101},
keywords = {steady Euler equations, transonic shock wave, spherically symmetric solutions, gravitational effect, implicit function differentiability theorem},
url = {https://www.sciopen.com/article/10.3934/era.2026225},
doi = {10.3934/era.2026225},
abstract = {In this paper, we adopted the steady compressible Euler system with a gravitational term as the governing equations, and focused on the effect of gravity on the transonic shock position in a three-dimensional spherically symmetric divergent nozzle. For a fixed supersonic inflow at the nozzle inlet, we proved that if the outlet pressure fell within an appropriate interval and the gravitational parameter    K was sufficiently small, the shock position was uniquely determined by    K and the outlet pressure, and the shock position was a strictly decreasing and continuously differentiable function of    K.}
}