Smooth subsonic and transonic spiral flows with nonzero vorticity to steady Euler-Poisson system in concentric cylinders. (English) Zbl 07897517
Summary: 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.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76N15 | Gas dynamics (general theory) |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76G25 | General aerodynamics and subsonic flows |
| 76H05 | Transonic flows |
| 35L65 | Hyperbolic conservation laws |
| 35M10 | PDEs of mixed type |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35B07 | Axially symmetric solutions to PDEs |
| 35B20 | Perturbations in context of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
Euler-Poisson system; structural stability; smooth transonic spiral flows; subsonic spiral flows; deformation-curl-Poisson decompositionReferences:
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