论文标题
无限壁上轴向压缩的亚音速射流的存在和独特性
Existence and uniqueness of axially symmetric compressible subsonic jet impinging on an infinite wall
论文作者
论文摘要
本文涉及适当的度量理论，即从半无限长喷嘴出现的亚轴线对称射流的影响，到刚性壁上。流体运动由稳定的等凝Euler系统描述。我们表明，存在一个临界值$ m_ {cr}> 0 $，如果给定的质量通量小于$ m_ {cr} $，则在给定的半直线长喷嘴上发出了独特的平滑亚音轴向对称喷气，并撞到给定的不均匀的墙壁。轴向对称撞击射流的表面是一个自由边界，它平稳地从喷嘴的边缘脱离。结果表明，腔室和大气之间的压力差的独特选择可确保自由边界的连续拟合条件。此外，还获得了向下游撞击射流和自由表面的渐近行为和衰减特性。本文的主要结果解决了关于可压缩的轴向对称撞击射流的良好适合性的开放问题，这是A. Friedman在[FA2]第16章中提出的。我们证明的关键要素是基于与Bernoulli类型的自由边界的准线性椭圆方程的变异方法。
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 $M_{cr}>0$, if the given mass flux is less than $M_{cr}$, 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 [FA2]. The key ingredient of our proof is based on the variational method to the quasilinear elliptic equation with the Bernoulli's type free boundaries.
