Methods and Applications of Analysis

Volume 22 (2015)

Number 3

On analytic solutions of the Prandtl equations with Robin boundary condition in half space

Pages: 281 – 300

DOI: http://dx.doi.org/10.4310/MAA.2015.v22.n3.a3

Authors

Yutao Ding (Mathematical Sciences Center, Tsinghua University, Beijing, China)

Ning Jiang (Mathematical Sciences Center, Tsinghua University, Beijing, China; and School of Mathematics and Statistics, Wuhan University, Wuhan, China)

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 [34].

Keywords

Prandtl equation, analytic spaces, Robin boundary condition, well-posedness

2010 Mathematics Subject Classification

Primary 35M13. Secondary 35Q35, 76D03, 76D10, 76N20.

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