Transonic shocks for 3-D axisymmetric compressible inviscid flows in cylinders
Analysis of PDEs
2020-11-30 v4 Mathematical Physics
math.MP
Abstract
We establish the existence of an axisymmetric weak solution to the steady Euler system with a transonic shock, nonzero vorticity, and nonzero swirl in a three-dimensional cylinder. When prescribing the supersonic solution in the upstream region by axisymmetric functions with variable entropy and variable angular momentum density(=swirl), we construct such a solution by using a Helmholtz decomposition of the velocity field and the method of iteration. An iteration scheme is developed using a delicate decomposition of the Rankine-Hugoniot conditions on the transonic shock via Helmholtz decomposition.
Keywords
Cite
@article{arxiv.1910.10607,
title = {Transonic shocks for 3-D axisymmetric compressible inviscid flows in cylinders},
author = {Hyangdong Park and Hyeongyu Ryu},
journal= {arXiv preprint arXiv:1910.10607},
year = {2020}
}