TY - JOUR
T1 - Vector Fields of Cancellation for the Prandtl Operators
AU - Yang , Tong
JO - Communications in Mathematical Analysis and Applications
VL - 2
SP - 345
EP - 354
PY - 2022
DA - 2022/03
SN - 1
DO - http://doi.org/10.4208/cmaa.2022-0004
UR - https://global-sci.org/intro/article_detail/cmaa/20311.html
KW - Prandtl operators, cancellation mechanism, vector field of cancellation, well-posedness theory, structural assumptions.
AB - <p style="text-align: justify;">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.</p>