论文标题
在有限长的喷嘴中，跨度稳定可压缩欧拉流动的跨音速接触不连续性的稳定性
Stability of transonic contact discontinuity for two-dimensional steady compressible Euler flows in a finitely long nozzle
论文作者
论文摘要
我们认为在有限长的喷嘴中，二维稳定可压缩欧拉流动的跨性别接触不连续性的稳定性。这是关于跨触点不连续性的跨性别流量的混合型问题作为喷嘴中的自由边界的第一项工作。我们从Euler-Lagrangian转换开始，以拉直新坐标中的接触不连续性。但是，根据质量通量，在转化后，亚音速区域的上喷嘴壁变成了自由边界。然后，我们开发了新的想法和技术，以三个步骤解决自由结束问题：（1）我们修复了自由边界，并生成了一种新的迭代方案，以解决双曲线 - 纤维纤维纤维混合类型的相应固定边界价值问题，通过为一阶双胞胎方程和二阶非线性椭圆形方程构建一些强大的估计值（2）我们通过构造具有固定点的映射来更新新的自由边界； （3）我们通过逆拉格朗加亚坐标转换建立，原始的自由接口问题承认背景状态附近的独特的分段光滑的跨音速解决方案，该解决方案由平滑的亚音速流和平滑的超音速流动，具有触点不连续性。
We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact discontinuity as a free boundary in nozzles. We start with the Euler-Lagrangian transformation to straighten the contact discontinuity in the new coordinates. However, the upper nozzle wall in the subsonic region depending on the mass flux becomes a free boundary after the transformation. Then we develop new ideas and techniques to solve the free-boundary problem in three steps: (1) we fix the free boundary and generate a new iteration scheme to solve the corresponding fixed boundary value problem of the hyperbolic-elliptic mixed type by building some powerful estimates for both the first-order hyperbolic equation and a second-order nonlinear elliptic equation in a Lipschitz domain; (2) we update the new free boundary by constructing a mapping that has a fixed point; (3) we establish via the inverse Lagrangian coordinates transformation that the original free interface problem admits a unique piecewise smooth transonic solution near the background state, which consists of a smooth subsonic flow and a smooth supersonic flow with a contact discontinuity.
