On Analytic Solutions of the Prandtl Equations with Robin Boundary Condition in Half Space

TL;DR

This paper proves the existence and uniqueness of analytic solutions to the nonlinear Prandtl equations with Robin boundary conditions in a half space, using the Cauchy-Kowalewski theorem, relevant for fluid dynamics and boundary layer theory.

Contribution

It establishes the first rigorous proof of analytic solutions for Prandtl equations with Robin boundary conditions in half space, connecting to Navier-slip boundary conditions in fluid mechanics.

Findings

Existence of analytic solutions proved.

Uniqueness of solutions established.

Applicable to Navier-Stokes inviscid limit scenarios.

Abstract

The existence and uniqueness of the analytic solutions to the nonlinear Prandtl equations with Robin boundary condition on a half space are proved, based on an application of abstract Cauchy-Kowalewski theorem. These equations arise in the inviscid limit of incompressible Navier-Stokes equations with Navier-slip boundary condition in which the slip length is square root of viscosity, as formally derived in [26].