# Classical Solutions for the 3D Quasi-Geostrophic System on a Bounded Domain

## TL;DR

This paper proves the local-in-time existence of classical solutions for a 3D quasi-geostrophic flow model on bounded cylindrical domains, revisiting and extending previous work on inviscid geophysical fluid dynamics.

## Contribution

It establishes the existence of classical solutions for the 3D quasi-geostrophic system on bounded domains, providing a rigorous mathematical foundation for this model.

## Key findings

- Proved local-in-time existence of classical solutions.
- Revisited and extended previous models for 3D quasi-geostrophic flow.
- Provided mathematical rigor for inviscid geophysical fluid dynamics on bounded domains.

## Abstract

We revisit a model for three-dimensional, inviscid quasi-geostrophic flow on bounded, cylindrical domains introduced by the authors in \cite{nv18}. We prove the local-in-time existence of classical solutions.