In 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 Ush∈ W3,∞(0 , 1) holds true, with solutions that are Gevrey class 3 in the horizontal direction

Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip

De Anna F.
;
Scrobogna S.
2023-01-01

Abstract

In 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 Ush∈ W3,∞(0 , 1) holds true, with solutions that are Gevrey class 3 in the horizontal direction
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3073021
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