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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.12195 |
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Table of Contents:
- This paper concerns the structural stability of smooth cylindrically symmetric supersonic spiral flows with large angular velocity for the steady Euler-Poisson system in a concentric cylinder. We establish the existence and uniqueness of some smooth supersonic Euler-Poisson flows with nonzero angular velocity and vorticity including both cylindrical spiral flows and axisymmetric spiral flows. The deformation-curl-Poisson decomposition for the steady Euler-Poisson system is utilized to deal with the hyperbolic-elliptic mixed structure in the supersonic region. For smooth cylindrical supersonic spiral flows, the key point lies on the well-posedness of a boundary value problem for a linear second order hyperbolic-elliptic coupled system, which is achieved by finding an appropriate multiplier to obtain the important basic energy estimates. The nonlinear structural stability is established by designing a two-layer iteration and combining the estimates for the hyperbolic-elliptic system and the transport equations. For smooth axisymmetric supersonic spiral flows, we use the special structure of the steady Euler-Poisson system to derive a priori estimates of the linearized second order elliptic system, which enable us to establish the structural stability of the background supersonic flow within the class of axisymmetric flows.