Boundary Layer for a Class of Nonlinear Pipe Flow
Daozhi Han, Anna Mazzucato, Dongjuan Niu, Xiaoming Wang
We establish the mathematical validity of the Prandtl boundary layer theory for a family of (nonlinear) parallel pipe flow. The convergence is verified under various Sobolev norms, including the physically important space-time uniform norm, as well as the $L^\infty(H^1)$ norm. Higher order asymptotics is also studied.