2019/08/05 by Shangkun Weng, Weng, Shangkun, Chunjing Xie +3 · 3 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1908.01694
openalex publication_date 2019/08/05 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28
In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit pressure. Compared with the known results on the stability of transonic shocks, one of the major difficulties for the axisymmetric flows with swirls is that corner singularities near the intersection point of the shock surface and nozzle boundary and the artificial singularity near the axis appear simultaneously. One of the key points in the analysis for this paper is the introduction of an invertible Lagrangian transformation which can straighten the streamlines in the whole nozzle and help to represent the solutions of transport equations explicitly.