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Smooth Subsonic and Transonic Spiral Flows with Nonzero Vorticity to Steady Euler–Poisson System in Concentric Cylinders

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Abstract

Both smooth subsonic and transonic spiral flows to steady Euler–Poisson system with nonzero angular velocity and vorticity in a concentric cylinder are studied. On the one hand, we investigate the structural stability of smooth cylindrically symmetric subsonic flows under three-dimensional perturbations on the inner and outer cylinders. On the other hand, the structural stability of smooth transonic flows under the axi-symmetric perturbations is examined. There are no any restrictions on the background subsonic and transonic solutions. A deformation-curl-Poisson decomposition to the steady Euler–Poisson system is utilized to deal with the hyperbolic-elliptic mixed structure in the subsonic region. We emphasize that there is a special structure of the steady Euler–Poisson system which yields a priori estimates and uniqueness of the linearized elliptic system.

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Acknowledgements

Weng is supported by the National Natural Science Foundation of China 12071359, 12221001.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei Province, People’s Republic of China

    Shangkun Weng, Wengang Yang & Na Zhang

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  1. Shangkun Weng
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  2. Wengang Yang
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  3. Na Zhang
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Correspondence to Na Zhang.

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Communicated by Rustum Choksi.

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Weng, S., Yang, W. & Zhang, N. Smooth Subsonic and Transonic Spiral Flows with Nonzero Vorticity to Steady Euler–Poisson System in Concentric Cylinders. J Nonlinear Sci 34, 76 (2024). https://doi.org/10.1007/s00332-024-10057-z

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  • DOI: https://doi.org/10.1007/s00332-024-10057-z

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