论文标题
跨力流动的结构稳定性
Structural Stability of Transonic Shock Flows with an External Force
论文作者
论文摘要
本文致力于通过平坦喷嘴的跨音速冲击的结构稳定性，以使用外力进行二维稳定的可压缩流。我们首先，通过在上游流量是统一的超音速流动时在喷嘴出口处开出适当的压力，以外力规定适当的压力，从而，通过外力规定适当的压力，将一维的透射冲击溶液的存在和独特性。结果表明，外力有助于稳定扁平喷嘴中的跨音速冲击，而冲击位置则是唯一确定的。然后，当出口压力适当扰动时，我们关注这些跨性别SHOC溶液的结构稳定性。我们分析中的新成分之一是使用\ cite {wengx2019}中开发的稳定的欧拉系统的变形 - 折曲分解来处理跨性别者冲击问题。
This paper is devoted to the structural stability of a transonic shock passing through a flat nozzle for two-dimensional steady compressible flows with an external force. We first establish the existence and uniqueness of one dimensional transonic shock solutions to the steady Euler system with an external force by prescribing suitable pressure at the exit of the nozzle when the upstream flow is a uniform supersonic flow. It is shown that the external force helps to stabilize the transonic shock in flat nozzles and the shock position is uniquely determined. Then we are concerned with the structural stability of these transonic shoc solutions when the exit pressure is suitably perturbed. One of the new ingredients in our analysis is to use the deformation-curl decomposition to the steady Euler system developed in \cite{WengX2019} to deal with the transonic shock problem.
