3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space

Li, Weixi; Yang, Yongzhen

doi:10.4208/cmaa.2022-0007

Cited by 4 publications

(2 citation statements)

References 43 publications

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“…Here, we just mention some recent works attempting to explore the hyperbolic feature of some simplified semi-linear models ( cf. [1,24,29]) in order to investigage the wave type property that lead to some kind of stability effect compared to the parabolic counterparts. In addition, a quasi-linear model was recently studied by [19].…”

Section: Introductionmentioning

confidence: 99%

Gevrey Well-Posedness of the Hyperbolic Prandtl Equations

null¹,

Xu²

2022

CMR

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We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class 3 2 in the tangential variable and is analytic in the normal variable.

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Section: Introductionmentioning

confidence: 99%

Gevrey Well-Posedness of the Hyperbolic Prandtl Equations

null¹,

Xu²

2022

CMR

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show abstract

“…Here, we just mention some recent works attempting to explore the hyperbolic feature of some simplified semi-linear models (cf. [1,24,29]) in order to investigate the wave type property that lead to some kind of stability effect compared to the parabolic counterparts. In addition, a quasi-linear model was recently studied by [19].…”

Section: Introductionmentioning

confidence: 99%

Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations

Wei-Xi Li,

Tong Yang,

Ping Zhang

2023

CMAA

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We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class 3/2 in the tangential variable and is analytic in the normal variable.

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

De Anna,

Kortum,

Scrobogna

2023

J. Math. Fluid Mech.

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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 $$U_{\textrm{sh}}\in W^{3, \infty }(0,1)$$ U sh ∈ W 3 , ∞ ( 0 , 1 ) holds true, with solutions that are Gevrey class 3 in the horizontal direction.

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3D Hyperbolic Navier-Stokes Equations in a Thin Strip: Global Well-Posedness and Hydrostatic Limit in Gevrey Space

Cited by 4 publications

References 43 publications

Gevrey Well-Posedness of the Hyperbolic Prandtl Equations

Gevrey Well-Posedness of the Hyperbolic Prandtl Equations

Gevrey Well-Posedness of Quasi-Linear Hyperbolic Prandtl Equations

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

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