Global regularity for a rapidly rotating constrained convection model of tall columnar structure with weak dissipation

TL;DR

This paper proves the global regularity and well-posedness of a three-dimensional rapidly rotating convection model with weak dissipation, shedding light on the behavior of tall columnar structures in fluid dynamics.

Contribution

It establishes the global existence, uniqueness, and stability of solutions for a new fluid model describing rotating convection with weak dissipation.

Findings

Proves global regularity of the model.

Demonstrates continuous dependence on initial data.

Analyzes large-time behavior of solutions.

Abstract

We study a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. Global existence, uniqueness, continuous dependence on initial data, and large-time behavior of strong solutions are shown provided the model is regularized by a weak dissipation term.