标题： 三维稳态普朗特方程的结构稳定性 显示英文标题

标题： Structural stability of three dimensional steady Prandtl equation

摘要： 三维普朗特方程的适定性是一个由于二次流的出现而仍然悬而未决的开放问题，尽管已有在解析和Gevrey函数空间上的研究。 这个问题被作为奥利尼克和萨莫金的经典著作[43]中的第三个开放问题提出。 本文旨在通过引入一种新方法来研究包含著名布拉修斯解的背景剖面的结构稳定性，从而解决这一开放问题。 关键观察包括引入一些内在向量场和最大原理的新版本。 特别是，我们通过分析由向量场对易子产生的曲率型量来克服对称性破坏带来的困难。 显示英文摘要

摘要： The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the third open problem in the classical book by Oleinik and Samokhin [43]. This paper aims to address this open problem in the steady case by introducing a new approach to study the structural stability of background profile that includes the famous Blasius solutions. The key observations include the introduction of some intrinsic vector fields and new versions of maximum principle. In particular, we overcome the difficulties caused by symmetry breaking through the analysis on the curvature-type quantities generated by commutators of the vector fields.