Abstract
AbstractIn the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that the optimal regularity of Prandtl is given by the class Gevrey 2 along the horizontal direction. The goal of this paper is to overcome this barrier, by dealing with the linearisation of the so-called hyperbolic Prandtl equations in a strip domain. We prove that the local well-posedness around a general shear flow $$U_{\textrm{sh}}\in W^{3, \infty }(0,1)$$
U
sh
∈
W
3
,
∞
(
0
,
1
)
holds true, with solutions that are Gevrey class 3 in the horizontal direction.
Funder
Bayerische Forschungsallianz
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
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