Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Zhu, Shi-Yong, Wang, Ya-Guang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2325963797, G6334114574
OpenAlex ID: W7212270455