On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

TL;DR

This paper proves the global well-posedness of certain scaled anisotropic Navier-Stokes equations and justifies the hydrostatic limit in a 2-D strip with analytic data, advancing understanding of fluid dynamics in thin domains.

Contribution

It establishes the global existence and uniqueness of solutions for anisotropic and hydrostatic Navier-Stokes systems in a 2-D strip with small analytic data, and rigorously justifies the hydrostatic limit.

Findings

Global well-posedness of anisotropic Navier-Stokes in a 2-D strip.

Justification of the hydrostatic limit from anisotropic to hydrostatic Navier-Stokes.

Solutions exist and are unique with small analytic initial data.

Abstract

In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data.