Gevrey Well-Posedness of the Hyperbolic Prandtl Equations (Communications in Mathematical Research, 2022)
We study 2D and 3D Prandtl equations of degenerate hyperbolictype, and establish without any structural assumption the Gevrey well-posedness with Gevrey index ≤ 2. Compared with the classical parabolic Prandtlequations, the loss of the derivatives, caused by the hyperbolic feature coupledwith the degeneracy, cannot be overcame by virtue of the classical cancellation mechanism that developed for the parabolic counterpart. Inspired by theabstract Cauchy-Kowalewski theorem and by virtue of the hyperbolic feature,we give in this text a straightforward proof, basing on an elementary $L^2$ energyestimate. In particular our argument does not involve the cancellation mechanism used efficiently for the classical Prandtl equations.
Keywords: Hyperbolic Prandtl boundary layer; well-posedness; Gervey space; abstract Cauchy-Kowalewski theorem.