English

Long time well-posdness of Prandtl system with small and analytic initial data

Analysis of PDEs 2014-09-08 v1

Abstract

In this paper, we investigate the long time existence and uniqueness of small solution to d,d, for d=2,3,d=2,3, dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that dd dimensional Prandtl system has a unique solution with the life-span of which is greater than \e\f43\e^{-\f43} if both the initial data and the value on the boundary of the tangential velocity of the outflow are of size \e.\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.

Keywords

Cite

@article{arxiv.1409.1648,
  title  = {Long time well-posdness of Prandtl system with small and analytic initial data},
  author = {Ping Zhang and Zhifei Zhang},
  journal= {arXiv preprint arXiv:1409.1648},
  year   = {2014}
}