标题： 三维定常Prandtl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Prandtl方程的适定性由于次流动现象的存在仍然是一个突出的公开问题，尽管有研究集中在解析函数空间和Gevrey函数空间上。 Oleinik和Samokhin的经典著作[43]中将此问题列为第三个公开问题。 本文旨在通过引入一种新方法来研究背景流场的结构稳定性（包括著名的Blasius解）以解决稳态情况下的这一公开问题。 关键观察包括引入某些内在向量场和新的最大值原理版本。 特别是，我们通过分析由向量场交换子生成的曲率型量克服了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.