Hydrostatic limit of the Navier-Stokes-alpha model

TL;DR

This paper investigates the hydrostatic limit of the Navier-Stokes-alpha model in thin domains, deriving limit equations and proving global well-posedness for small initial data in analytic spaces.

Contribution

It introduces a new hydrostatic limit for the Navier-Stokes-alpha model and establishes global well-posedness results in a specialized setting.

Findings

Derived Prandtl-type limit equations for the model

Proved global well-posedness for small initial conditions

Validated the hydrostatic approximation in thin domains

Abstract

In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin striped domain. We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.