Transonic shocks for steady Euler flows with an external force in an axisymmetric perturbed cylinder

• DOI: 10.48550/arxiv.2404.14652
• Publication Date: 2024-04-22
• Authors: Zihao Zhang
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; Analysis of PDEs (math.AP)

We concern the structural stability of transonic shocks for steady Euler system with an external force in axisymmetric perturbed cylinder. For a class forces, we first prove existence and uniqueness shock solution to one-dimensional force, which shows that has stabilization effect on flat cylinder position is uniquely determined. then establish under perturbations incoming supersonic flow, nozzle boundary, exit pressure force. Different from problem two-dimensional nozzles, there exists singularity along symmetric axis flows. introduce invertible modified Lagrangian transformation overcome this difficulty straighten streamline. One key elements analysis utilize deformation-curl decomposition effectively decouple hyperbolic elliptic modes Another one equivalent reformulation Rankine-Hugoniot conditions so front determined by algebraic equation.