article

Title: Boundary layer associated with a class of 3D nonlinear plane parallel channel flows

Authors: Anna L. Mazzucato, Dongjuan Niu and Xiaoming Wang

Issue: Volume 60 (2011), Issue 4, 1113-1136

Abstract:

We establish the mathematical validity of the Prandtl boundary layer theory for a family of (nonlinear) plane parallel flow. The convergence is proved under various Sobolev norms, including the physically important space-time uniform norm, as well as the $L^infty(H^1)$ norm. Higher-order asymptotics are also considered.