发表机构
College of Mathematics and Systems Science, Shandong University of Science and Technology; School of Mathematical Sciences, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University（山东科技大学数学与系统科学学院; 上海交通大学数学科学学院，教育部低维材料物理化学重点实验室和上海市应用数学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过新迭代格式和线性消去法，证明具有退化临界点的Prandtl方程在Sobolev空间中局部适定，表明Oleinik单调性条件非必要，零剪切应力不必然导致边界层分离。
AI 中文摘要
本文致力于研究经典Prandtl方程在有限阶Sobolev空间中的适定性。对于具有退化临界点和一般外流的初始数据，通过引入新的迭代格式和线性消去法，我们得到了Prandtl方程在Sobolev空间中解的局部时间存在性和唯一性。该结果表明，Oleinik单调性条件并非Prandtl方程在Sobolev空间中适定的必要条件，并为证明零剪切应力不一定导致二维非定常边界层中的边界层分离提供了证据。
英文摘要
This paper is devoted to the well-posedness of classical Prandtl equations in a finite order Sobolev space. For a initial data with degenerate critical points and general outflow, we obtain the local-in-time existence and uniqueness of the solution to the Prandtl equations in a Sobolev space, by introducing a new iteration scheme and linear cancelation. This result shows that Oleinik's monotonicity condition is not a necessary condition for the Prandtl equations to be well-posed in Sobolev spaces and provides evidence to demonstrate that zero shear stress does not necessarily lead to boundary layer separation in two-dimensional unsteady boundary layers.
