Title: Gevrey-class-3 regularity of the linearised hyperbolic Prandtl system on a strip Show Chinese title

Title: 线性化双曲普朗特系统在条带上的Gevrey类3正则性

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. Show Chinese abstract

Abstract: 在本文中，我们研究了在剪切流周围线性化普朗特方程的一个具有物理意义的扩展。 在没有任何结构假设的情况下，众所周知，普朗特方程的最佳正则性在水平方向上由Gevrey 2类给出。 本文的目标是通过处理所谓的双曲普朗特方程在条带区域内的线性化来克服这一障碍。 我们证明了在一般剪切流附近局部适定性成立，解在水平方向上属于Gevrey 3类。