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Steady Prandtl Boundary Layer Expansions Over a Rotating Disk

Archive for Rational Mechanics and Analysis volume 224, pages 421–469 (2017)Cite this article

Abstract

This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier-Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid limit. In so doing, we develop a new set of function spaces and prove several embedding theorems which capture the interaction between the Prandtl scaling and the geometry of our domain.

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Authors and Affiliations

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

    Sameer Iyer

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  1. Sameer Iyer
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Correspondence to Sameer Iyer.

Additional information

Communicated by V. Šverák

Partially supported by NSF Grant 1209437.

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Iyer, S. Steady Prandtl Boundary Layer Expansions Over a Rotating Disk. Arch Rational Mech Anal 224, 421–469 (2017). https://doi.org/10.1007/s00205-017-1080-9

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  • DOI: https://doi.org/10.1007/s00205-017-1080-9

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