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arXiv · 2203.08988

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

Zhouping Xin·Liqun Zhang·Junning Zhao
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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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Zhouping Xin, Liqun Zhang, Junning Zhao. 2022-03-16. Global Well-posedness and Regularity of Weak Solutions to the Prandtl's System. https://arxiv.org/abs/2203.08988

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