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Autori principali: Wang, Chunpeng, Zhang, Zihao
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2505.12195
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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
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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