Hydrostatic approximation of the 2D primitive equations in a thin strip

TL;DR

This paper proves the global well-posedness of 2D primitive equations in a thin strip with analytic data and analyzes the hydrostatic limit, linking it to a Prandtl-like system and a transport-diffusion equation.

Contribution

It establishes the global well-posedness for the 2D primitive equations in a thin strip and rigorously derives the hydrostatic limit as the strip width approaches zero.

Findings

Global well-posedness for small analytic data

Hydrostatic limit yields a Prandtl-like system

Limit involves a transport-diffusion equation

Abstract

We prove the global wellposedness of the 2D non-rotating primitive equations with no-slip boundary conditions in a thin strip of width $\eps$ for small data which are analytic in the tangential direction. We also prove that the hydrostatic limit (when $\eps \to 0$) is a couple of a Prandtl-like system for the velocity with a transport-diffusion equation for the temperature.