Remarks on the Prandtl boundary layer

Remarks on Boundary Layer Expansions

3 Boundary layer sizes and equations 17 3.1 Definitions and hypothesis (H4) . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Solvability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2.1 Order zero operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.2 Operators with constant coefficients . . . . . . . . . . . . . . . . . . . 19 3...

Almost Global Existence for the Prandtl Boundary Layer Equations

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within ε of a stable profile, then the unique solution of the C...

Some Remarks on the Flat Plate Boundary Layer*

A Note on the Prandtl Boundary Layers

Abstract. This note concerns a nonlinear ill-posedness of the Prandtl equation and an invalidity of asymptotic boundary-layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear ill-posedness results established by Gérard-Varet and Dormy [2], and an analysis in Guo and Tice [5]. We show that the asymptotic boundary-layer expansion ...

On the Local Existence of Analytic Solutions to the Prandtl Boundary Layer Equations

ABSTRACT. We address the local well-posedness of the Prandtl boundary layer equations. Using a new change of variables we allow for more general data than previously considered, that is, we require the matching at the top of the boundary layer to be at a polynomial rather than exponential rate. The proof is direct, via analytic energy estimates in the tangential variables. Communications in Mat...