论文标题
固定亚音线索可压缩欧拉的稳定性在二维直道中具有质量增加的稳定性
Stability of Stationary Subsonic Compressible Euler Flows with Mass-Additions in Two-Dimensional Straight Ducts
论文作者
论文摘要
我们显示了一系列固定的亚音话压缩欧拉家族的存在，独特性和稳定性，并在二维直流管中进行质量增加，并受到适当的时间与时间无关的多维边界条件，并在入口处出现。通常的方法基于质量和拉格朗日坐标的保护，以分离系统的椭圆形和双曲线模式。我们建立了一个新的分解和非线性迭代计划，以克服这一主要困难。它揭示了质量中的质量中的质量和双曲线模式中引入非常强的相互作用，并导致一类具有多个积分非本地术语的二阶椭圆方程。在傅立叶分析方法应用后，通过研究无限耦合边界问题的无限耦合边界问题的无限耦合边界值问题来解决线性问题。
We show existence, uniqueness and stability for a family of stationary subsonic compressible Euler flows with mass-additions in two-dimensional rectilinear ducts, subjected to suitable time-independent multi-dimensional boundary conditions at the entrances and exits.The stationary subsonic Euler equations consist a quasi-linear system of elliptic-hyperbolic composite-mixed type, while addition-of-mass destructs the usual methods based upon conservation of mass and Lagrangian coordinates to separate the elliptical and hyperbolic modes of the system. We establish a new decomposition and nonlinear iteration scheme to overcome this major difficulty. It reveals that mass-additions introduce very strong interactions in the elliptic and hyperbolic modes, and lead to a class of second-order elliptic equations with multiple integral nonlocal terms. The linearized problem is solved by studying algebraicand analytical properties of infinite weakly coupled boundary-value problems of ordinary differential equations, each with multiple nonlocal terms, after applications of Fourier analysis methods.
