Steady Prandtl Boundary Layer Expansions Over a Rotating Disk

Stationary inviscid limit to shear flows

“…In the presence of boundaries, the vanishing viscosity asymptotics are a major open problem in fluids made challenging due to the mismatch between the no-slip condition u ε | ∂Ω = 0 and the no penetration condition typically satisfied by Euler flows: u 0 · n = 0. This mismatch is typically rectified by the presence of Prandtl's boundary layer (see [GN17], [Iy17a], [Iy16], [Iy17b] for relevant results in the 2D stationary setting). In this article, we will consider Euler flows that themselves satisfy no-slip:…”

Steady Prandtl Layers Over a Moving Boundary: Nonshear Euler Flows

“…A central task in this setting is to establish validity of an expansion of the type (1.5), and this is considered to be one of the most challenging open problems in fluid mechanics. It has been achieved in the setting of a moving boundary in [GN14], [Iy15], [Iy16]. The method introduced by [GN14] relies on establishing a crucial positivity estimate which gives o(1) control over the remainder quantity ||v y ,…”

“…Such a flow is non-shear, as in the set-up considered here. In the simpler case when the flows are actually circular (and therefore shear), as opposed to horizontal, in the presence of a rotating disk, the article of [Iy15] develops machinery to handle the geometry of the boundary. The present article can be viewed as a first step in studying non-shear flows, without adding the complexities of a curved boundary.…”

Boundary layer for 3D nonlinear parallel pipe flow of nonhomogeneous incompressible Navier‐Stokes equations

“…A similar result over a rotating disk was obtained by Iyer. 18 The Sobolev stability for the steady Navier-Stokes flow was obtained by Gérard-Varet et al 19 Very recently, Guo and Iyer 20 proved the validity of steady Prandtl layer expansion, which removes the moving boundary condition of Guo et al 17 For the time-dependent case, Sammartino and Caflisch 21,22 obtained the local existence of analytic solutions of Prandtl equations and a rigorous theory on the stability of boundary layers for incompressible flow. Han et al 23 verified the validity of the boundary layer theory for a class of nonlinear pipe flow.…”