Global Well-posedness and Regularity of Weak Solutions to the Prandtl's System
Analysis of PDEs
2022-05-04 v2
Abstract
We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we gave a direct proof of existence of a global weak solution by a direct BV estimate. Then we prove the uniqueness and continuous dependence on data of such a weak solution to the initial-boundary value problem. Finally, we show the smoothness of the weak solutions and then the global existence of smooth solutions.
Keywords
Cite
@article{arxiv.2203.08988,
title = {Global Well-posedness and Regularity of Weak Solutions to the Prandtl's System},
author = {Zhouping Xin and Liqun Zhang and Junning Zhao},
journal= {arXiv preprint arXiv:2203.08988},
year = {2022}
}