Long time well-posdness of Prandtl system with small and analytic initial data
arXiv:1409.1648
Abstract
In this paper, we investigate the long time existence and uniqueness of small solution to for dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that dimensional Prandtl system has a unique solution with the life-span of which is greater than $\e^{-\f43}$ if both the initial data and the value on the boundary of the tangential velocity of the outflow are of size $\e.$ We mention that the tool developed in \cite{Ch04, CGP} to make the analytical type estimates and the special structure of the nonlinear terms to this system play an essential role in the proof of this result.