薄带中的三维双曲Navier-Stokes方程:Gevrey空间中的全局适定性和流体静力极限

Communications in Mathematical Analysis and Applications Pub Date : 2022-04-20 DOI:10.4208/cmaa.2022-0007

Wei-Xi Li, Tong Yang

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引用次数: 2

摘要

我们考虑了三维各向异性Naver-Stokes方程在薄带上的双曲版本及其流体静力极限，即双曲Prandtl型方程。我们证明了这两个系统在时间上的全局存在唯一性，以及当初始数据属于索引为2的Gevrey函数空间时的静力极限。该证明是基于直接能量法，通过观察系统中的阻尼效应。

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

We consider the hyperbolic version of three-dimensional anisotropic Naver-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping e ﬀ ect in the systems.

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Communications in Mathematical Analysis and Applications

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