Steady Prandtl Boundary Layer Expansion of Navier-Stokes Flows over a Rotating Disk

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.

version 2: 94 pages, shorter construction in Section 3.2, results unchanged

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