The van Dommelen and Shen singularity in the Prandtl equations

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• 作者：Igor Kukavica^a ; ^{kukavica@usc.edu} ; Vlad Vicol^b ; ^{vvicol@math.princeton.edu} ; Fei Wang^a ; ^{wang828@usc.edu}
• 关键词：Prandtl equations ; Boundary layer separation
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：307
• 期：Complete
• 页码：288-311
• 全文大小：472 K
• 卷排序：307

文摘

In 1980, van Dommelen and Shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the Prandtl boundary layer equations from a smooth initial datum, for a nontrivial Euler background. In this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness.