Prandtl算子消去的向量场
Vector fields of Cancellation for the Prandtl Operators
摘要：
1904年导出的Prandtl方程的适定性问题一直是边界层理论研究中的一个热点问题。最近，人们提出了一些新的思想，通过消去法来克服切向导数的损失，从而证明了Prandtl方程在索伯列夫空间中的适定性，避免了Oleinik经典工作中的Crocco变换.这个简短的说明旨在表明，抵消机制实际上是有关的一些内在的方向导数，可以用来恢复切向导数下的一些结构假设的流体附近的边界。
英文摘要：
It has been a fascinating topic in the study of boundary layer theory about the well-posedness of Prandtl equation that was derived in 1904. Recently, new ideas about cancellation to overcome the loss of tangential derivatives were obtained so that Prandtl equation can be shown to be well-posed in Sobolev spaces to avoid the use of Crocco transformation as in the classical work of Oleinik. This short note aims to show that the cancellation mechanism is in fact related to some intrinsic directional derivative that can be used to recover the tangential derivative under some structural assumption on the fluid near the boundary.
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