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

Author:

De Anna FrancescoORCID,Kortum Joshua,Scrobogna Stefano

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

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-11-06

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