Global Well-posedness and Regularity of Weak Solutions to the Prandtl's System

2022/03/16 by Xin, Zhouping, Zhang, Liqun, Zhao, Junning · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.08988

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.

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• Well-posedness of the compressible boundary layer equations with analytic initial data

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