Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points

Shi-Yong Zhu; Ya-Guang Wang

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arXiv · 2609.10936

Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points

Shi-Yong Zhu·Ya-Guang Wang

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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.

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Shi-Yong Zhu, Ya-Guang Wang. 2026-09-10. Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points. https://arxiv.org/abs/2609.10936

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