  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.
