Transonic shocks for 3-D axisymmetric compressible inviscid flows in cylinders

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Park, Hyangdong¹  Ryu, Hyeongyu² 

[1] Yonsei Univ, Ctr Math Anal & Computat CMAC, 50 Yonsei Ro, Seoul 03722, South Korea

[2] POSTECH, Dept Math, 77 Cheongam Ro, Pohang 37673, Gyeongbuk, South Korea

关键词: Axisymmetric;    Free boundary problem;    Helmholtz decomposition;    Steady Euler system;    Swirl;    Transonic;    shock;   

DOI  :  10.1016/j.jde.2020.06.016

来源: Elsevier

【 摘 要 】

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 super- sonic 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 ve- locity 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.

【 授权许可】

Free