Sonic-supersonic solutions for the two-dimensional steady full Euler equations
Abstract
This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves for the two-dimensional full Euler equations in gas dynamics. In order to deal with the parabolic degeneracy near the sonic curve, a novel set of dependent and independent variables are introduced to transform the Euler equations into a new system of governing equations which displays a clear regularity-singularity structure. With the help of technical characteristic decompositions, the existence of a local smooth solution for the new system is first established in a weighted metric space by using the iteration method and then expressed in terms of the original physical variables. This is the first time to construct a classical sonic-supersonic solution near a sonic curve for the full Euler equations.
Cite
@article{arxiv.1909.10156,
title = {Sonic-supersonic solutions for the two-dimensional steady full Euler equations},
author = {Yanbo Hu and Jiequan Li},
journal= {arXiv preprint arXiv:1909.10156},
year = {2019}
}