| Autor: |
Fang, Beixiang, Gao, Xin, Xiang, Wei, Zhao, Qin |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper is concerned with the existence and location of three-dimensional axisymmetric transonic shock with large swirl velocity for solutions of the steady compressible full Euler system in a cylindrical nozzle with prescribed receiver pressure. Special non-trivial shock solutions with large vorticity are first constructed by considering arbitrarily given non-zero swirl functions. Then the existence and locations of the transonic shock solutions to the full Euler equations are achieved under small perturbations on the special shock solutions with appropriate boundary conditions on the entrance of the nozzle and the receiver pressure at the exit. Moreover, within the proof, fundamental contributions of the non-zero swirl velocity in determining the position of the shock front are investigated. Mathematically, it can be formulated as a free boundary value problem with the shock front as the free boundary, whose solution states are a perturbation of non-trivial background solutions, and with a singularity at the axis-symmetry. Because the shock location can be arbitrary for the special shock solutions, approximate shock solutions of a free boundary problem for a specific linearized Euler system are constructed and an iteration scheme is designed around the approximate shock solution with a perturbation of higher order. As far as we know, it is the first mathematical result on the three-dimensional transonic shock with either large vorticity or large swirl velocity. New ideas and methods introduced in this paper will be also helpful for other problems with similar difficulties. |
| Databáze: |
arXiv |
| Externí odkaz: |
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