标题： 稳态三段层方程解的存在性与唯一性 显示英文标题

标题： Existence and Uniqueness of Solutions for Steady Triple-Deck Equations

摘要： 三重层结构在边界层流动中出现，当小的局部壁面扰动引起中等程度的平均流变形时。 该领域现有的大多数研究集中于该系统的渐近解和数值解的推导，而严格的数学结果仍然很少。 在本文中，我们首次建立了稳态三重层方程解的存在性和唯一性。 稳态三重层方程可以通过傅里叶变换简化为一个以频率为参数的艾里方程。 主要困难在于艾里方程在零频率处退化，阻碍了相对于频率参数的解的统一估计。 一个关键贡献是我们发现了一个涉及贝塞尔函数零点分布的微妙函数，通过分析艾里函数的结构来克服退化问题。 此外，我们推导了一个高频估计，并修改了一个椭圆乘子以获得解的统一估计。 显示英文摘要

摘要： Triple-deck structures arise in boundary-layer flows when small localized wall perturbations induce moderate mean-flow distortion. Most existing studies in this field focus on the derivations of the asymptotic and numerical solutions of this system, while rigorous mathematical results remain scarce. In this paper, we establish, for the first time, the existence and uniqueness of the solutions to the steady triple-deck equations. The steady triple-deck equations can be reduced to an Airy equation with frequency as a parameter via Fourier transformation. The main difficulty is that the Airy equation degenerates at zero frequency, hindering uniform estimates of the solution with respect to the frequency parameter. A key contribution is that we find a subtle function involving the distribution of zeros of the Bessel function to overcome the degeneracy by analyzing the structure of the Airy function. Additionally, we derive a higher-frequency estimate and modify an elliptic multiplier to obtain uniform estimates of the solution.