3D hyperbolic Navier-Stokes equations in a thin strip: global well-posedness and hydrostatic limit in Gevrey space

TL;DR

This paper establishes the global well-posedness and hydrostatic limit of 3D hyperbolic Navier-Stokes equations in a thin strip within Gevrey spaces, using energy methods to analyze damping effects.

Contribution

It proves the global existence, uniqueness, and hydrostatic limit for hyperbolic 3D anisotropic Navier-Stokes equations in a thin strip in Gevrey spaces, a novel analysis for such systems.

Findings

Global well-posedness of the hyperbolic Navier-Stokes system

Convergence to hydrostatic limit in Gevrey space

Energy method reveals damping effects in the system

Abstract

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 effect in the systems.