A remark on a priori estimate for the Navier-Stokes equations with the Coriolis force

TL;DR

This paper extends an a priori estimate for the Navier-Stokes equations to include the Coriolis force, proving global existence and analyzing asymptotic behavior of solutions regardless of rotation speed.

Contribution

It demonstrates that the a priori estimate by Lei and Lin applies even with the Coriolis force, leading to new results on global solutions and their asymptotics.

Findings

A priori estimate holds with Coriolis force

Existence of unique global solutions for any rotation speed

Analysis of solutions' asymptotic behavior

Abstract

The Cauchy problem for the Navier-Stokes equations with the Coriolis force is considered. It is proved that a similar a priori estimate, which is derived for the Navier-Stokes equations by Lei and Lin [11], holds under the effect of the Coriolis force. As an application existence of a unique global solution for arbitrary speed of rotation is proved, as well as its asymptotic behavior.