PreprintCC BY 4.0arXiv
Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points
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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BibTeX
@misc{zhu2026wellposedness,
title = {{Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points}},
author = {Shi-Yong Zhu and Ya-Guang Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10936},
eprint = {2609.10936},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10936},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Well-posedness of the two-dimensional unsteady Prandtl system in Sobolev space with degenerate critical points
AU - Shi-Yong Zhu
AU - Ya-Guang Wang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.10936
UR - https://arxiv.org/abs/2609.10936
AB - 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.
ER -