# Mathematical study of the equatorial Ekman boundary layer

## TL;DR

This paper analyzes a mathematical model of the equatorial Ekman boundary layer in rotating fluids, establishing well-posedness, uniqueness, and boundary conditions for the degenerate elliptic equations involved.

## Contribution

It provides the first rigorous mathematical analysis of a simplified boundary layer model near the equator for rotating fluids.

## Key findings

- Existence of solutions via Lax-Milgram lemma
- Uniqueness under additional integrability conditions
- Transparent boundary condition formulation

## Abstract

In this paper we study the well-posedness of a simple model of boundary layer for rotating fluids between two concentric spheres near the equator. We show that this model can be seen as a degenerate elliptic equation , for which we prove an existence result thanks to a Lax-Milgram type lemma. We also prove uniqueness under an additional integrability assumption and present a transparent boundary condition for such layers.