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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2505.12195 |
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| _version_ | 1866918045905059840 |
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| author | Wang, Chunpeng Zhang, Zihao |
| author_facet | Wang, Chunpeng Zhang, Zihao |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural stability of supersonic spiral flows with large angular velocity for the Euler-Poisson system Wang, Chunpeng Zhang, Zihao Analysis of PDEs 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. |
| title | Structural stability of supersonic spiral flows with large angular velocity for the Euler-Poisson system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.12195 |