TY - JOUR
T1 - Gevrey Well-Posedness of the Hyperbolic Prandtl Equations
AU - Li , Wei-Xi
AU - Xu , Rui
JO - Communications in Mathematical Research 
VL - 4
SP - 605
EP - 624
PY - 2022
DA - 2022/10
SN - 38
DO - http://doi.org/10.4208/cmr.2021-0104
UR - https://global-sci.org/intro/article_detail/cmr/21074.html
KW - Hyperbolic Prandtl boundary layer, well-posedness, Gervey space, abstract Cauchy-Kowalewski theorem.
AB - <p style="text-align: justify;">We study 2D and 3D Prandtl equations of degenerate hyperbolic
type, and establish without any structural assumption the Gevrey well-posedness with Gevrey index ≤ 2. Compared with the classical parabolic Prandtl
equations, the loss of the derivatives, caused by the hyperbolic feature coupled
with the degeneracy, cannot be overcame by virtue of the classical cancellation mechanism that developed for the parabolic counterpart. Inspired by the
abstract Cauchy-Kowalewski theorem and by virtue of the hyperbolic feature,
we give in this text a straightforward proof, basing on an elementary $L^2$ energy
estimate. In particular our argument does not involve the cancellation mechanism used efficiently for the classical Prandtl equations.</p>