Geodesic
Existence and uniqueness of axially symmetric compressible subsonic jet impinging on an infinite wall
Jianfeng Cheng1 ; Lili Du1 ; Qin Zhang2
1Sichuan University, Chengdu, China
2Chongqing Jiaotong University, China
Interfaces and free boundaries, Tome 23 (2021) no. 1, pp. 1-58

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This paper is concerned with the well-posedness theory of the impact of a subsonic axially symmetric jet emerging from a semi-infinitely long nozzle, onto a rigid wall. The fluid motion is described by the steady isentropic Euler system. We showed that there exists a critical value Mcr​>0, if the given mass flux is less than Mcr​, there exists a unique smooth subsonic axially symmetric jet issuing from the given semi-infinitely long nozzle and hitting a given uneven wall. The surface of the axially symmetric impinging jet is a free boundary, which detaches from the edge of the nozzle smoothly. It is showed that a unique suitable choice of the pressure difference between the chamber and the atmosphere guarantees the continuous fit condition of the free boundary. Moreover, the asymptotic behaviors and the decay properties of the impinging jet and the free surface in downstream were also obtained. The main results in this paper solved the open problem on the well-posedness of the compressible axially symmetric impinging jet, which has proposed by A. Friedman in Chapter 16 in [26]. The key ingredient of our proof is based on the variational method to the quasilinear elliptic equation with the Bernoulli’s type free boundaries.
DOI : 10.4171/ifb/449
Classification : 76-XX, 35-XX
Mots-clés : Existence and uniqueness, free streamline, compressible Euler system, subsonic impinging flow

Jianfeng Cheng  1   ; Lili Du  1   ; Qin Zhang  2

1 Sichuan University, Chengdu, China
2 Chongqing Jiaotong University, China 
Jianfeng Cheng; Lili Du; Qin Zhang. Existence and uniqueness of axially symmetric compressible subsonic jet impinging on an infinite wall. Interfaces and free boundaries, Tome 23 (2021) no. 1, pp. 1-58. doi: 10.4171/ifb/449
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     title = {Existence and uniqueness of axially symmetric compressible subsonic jet impinging on an infinite wall},
     journal = {Interfaces and free boundaries},
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     year = {2021},
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     number = {1},
     doi = {10.4171/ifb/449},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/449/}
}
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