Gevrey-class-3 regularity of the linearised hyperbolic Prandtl system on a strip

TL;DR

This paper proves that solutions to the linearised hyperbolic Prandtl system in a strip domain are Gevrey class 3 in the horizontal direction, extending regularity results beyond the classical Gevrey 2 class.

Contribution

It establishes Gevrey class 3 regularity for the linearised hyperbolic Prandtl equations without structural assumptions, surpassing the known Gevrey 2 barrier.

Findings

Solutions are Gevrey class 3 in the horizontal direction.

Local well-posedness holds for general shear flows.

Extends regularity results for hyperbolic Prandtl equations.

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 holds true, with solutions that are Gevrey class 3 in the horizontal direction.