二维无限长发散喷管中的连续声速-超声速流

中文摘要 AI 辅助

本文研究具有直固体壁面的二维无限长发散喷管中的连续声速-超声速流。对于给定的入口，该入口是圆心位于喷管顶点的圆弧的小扰动，我们建立了连续声速-超声速势流的全局存在性和唯一性，该流动接近于径向对称的声速-超声速流。流动在入口处为声速，速度沿法线方向，并在喷管内变为超声速。这种声速-超声速模型由拟线性非严格双曲方程控制，该方程在入口处具有退化性，且这种退化是弱的，其意义在于从每个声速点（壁面处的点除外）恰好有两条不同的特征线指向超声速区域。分析的关键要素之一是通过特征线法获得声速入口附近的精确渐近行为，这对于建立连续声速-超声速流的局部存在性至关重要。另一个关键要素是将局部解全局延拓并在超声速区域推导一致估计。

英文摘要

This paper concerns continuous sonic-supersonic flows in a two-dimensional infinitely long divergent nozzle with straight solid walls. For a given inlet that is a small perturbation of an arc centered at the vertex of the nozzle, we establish the global existence and uniqueness of a continuous sonic-supersonic potential flow which is close to the radially symmetric sonic-supersonic flow. The flow is sonic at the inlet, with its velocity along the normal direction, and becomes supersonic in the nozzle. Such a sonic-supersonic model is governed by a quasilinear nonstrictly hyperbolic equation with degeneracy at the inlet, and the degeneracy is weak in the sense that there exist exactly two distinct characteristics from each sonic point, except for those at the walls, pointing into the supersonic region. One of the crucial ingredients of the analysis is to obtain the precise asymptotic behavior near the sonic inlet by the method of characteristics, which is essential for establishing the local existence of continuous sonic-supersonic flows. Another one is to extend the local solution globally and derive uniform estimates in the supersonic region.

发表机构

• School of Mathematics, Jilin University（吉林大学数学学院）

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