# Boundary Layer Study for an Ocean Related System with a Small Viscosity Parameter

## TL;DR

This paper investigates the behavior of a linearized ocean system with small viscosity, establishing convergence results and boundary layer thickness estimates as viscosity approaches zero.

## Contribution

It provides the first rigorous analysis of boundary layer effects and convergence for the linearized primitive equations with small viscosity.

## Key findings

- Proves $L^
abla$ convergence as viscosity tends to zero.
- Estimates the boundary layer thickness in the system.
- Analyzes the impact of small viscosity on the system's behavior.

## Abstract

We study an ocean related system with a small viscosity parameter, which is the linearized version of the modified Primitive Equations. As the parameter goes to zero, a $L^\infty$ convergence result is obtained together with the estimation on the thickness of the boundary layer.