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Prandtl Boundary Layer Expansions of Steady Navier–Stokes Flows Over a Moving Plate

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Abstract

This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier–Stokes flows. The stationary flows, with small viscosity, are considered on \([0,L]\times \mathbb {R}_{+}\), with a no-slip boundary condition over a moving plate at \(y=0\). We establish the validity of the Prandtl boundary layer expansion and its error estimates.

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Acknowledgements

The authors wish to thank H. Dong, J. Guzman, and I. Tice for their discussions and pointing out references [2, 17, 18] on regularity of Stokes problems in a domain with corners. They also thank the referees and Sameer Iyer for their careful readings and constructive comments to improve the final presentation of the paper. Y. Guo’s research is supported in part by NSFC Grant 10828103, NSF Grant DMS-1209437, NSF Grant DMS-1611695, and a Simon Fellowship, and T. Nguyen’s research was supported in part by the NSF under Grants DMS-1108821 and DMS-1405728.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George street, Providence, RI, 02912, USA

    Yan Guo

  2. Department of Mathematics, Pennsylvania State University, State College, PA, 16802, USA

    Toan T. Nguyen

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  1. Yan Guo
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  2. Toan T. Nguyen
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Correspondence to Toan T. Nguyen.

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Guo, Y., Nguyen, T.T. Prandtl Boundary Layer Expansions of Steady Navier–Stokes Flows Over a Moving Plate. Ann. PDE 3, 10 (2017). https://doi.org/10.1007/s40818-016-0020-6

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  • DOI: https://doi.org/10.1007/s40818-016-0020-6

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