Global Existence and Long-Time Asymptotics for Rotating Fluids in a 3D Layer

TL;DR

This paper investigates the behavior of rotating fluid flows in a 3D layer, proving global existence of solutions with large rotation and their convergence to 2D vortices over time.

Contribution

It establishes the global existence of solutions for the Navier-Stokes-Coriolis system in a 3D layer with large rotation, and describes their asymptotic convergence to vortices.

Findings

Existence of global solutions with large angular velocity

Solutions converge to 2D Lamb-Oseen vortices over time

Results apply to infinite-energy flows with nonzero circulation

Abstract

The Navier-Stokes-Coriolis system is a simple model for rotating fluids, which allows to study the influence of the Coriolis force on the dynamics of three-dimensional flows. In this paper, we consider the NSC system in an infinite three-dimensional layer delimited by two horizontal planes, with periodic boundary conditions in the vertical direction. If the angular velocity parameter is sufficiently large, depending on the initial data, we prove the existence of global, infinite-energy solutions with nonzero circulation number. We also show that these solutions converge toward two-dimensional Lamb-Oseen vortices as time goes to infinity.