TY - JOUR
T1 - Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations
AU - Li , Wei-Xi
AU - Yang , Tong
AU - Zhang , Ping
JO - Communications in Mathematical Analysis and Applications
VL - 4
SP - 388
EP - 420
PY - 2023
DA - 2023/11
SN - 2
DO - http://doi.org/10.4208/cmaa.2023-0007
UR - https://global-sci.org/intro/article_detail/cmaa/22148.html
KW - Hyperbolic Prandtl equations, quasi-linear, Gevrey class.
AB - <p style="text-align: justify;">We study the hyperbolic version of the Prandtl system derived from
the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic
Prandtl equation leads to an additional instability mechanism. To overcome
the loss of derivatives in all directions in the quasi-linear term, we introduce
a new auxiliary function for the well-posedness of the system in an anisotropic
Gevrey space which is Gevrey class 3/2 in the tangential variable and is analytic in the normal variable.</p>