On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations

TL;DR

This paper investigates how a strong Coriolis force influences the existence and uniqueness of solutions to the stationary Navier-Stokes equations, revealing dispersive effects distinct from the non-stationary case.

Contribution

It introduces a new Fourier-Besov space framework to analyze the dispersive effects of the Coriolis force on stationary Navier-Stokes equations, establishing existence and uniqueness results.

Findings

Existence of unique solutions for large external forces with sufficiently strong Coriolis force.

Dispersive effects of the Coriolis force differ from non-stationary cases.

Classical results for non-stationary Navier-Stokes are extended to the stationary case.

Abstract

The dispersive effect of the Coriolis force for the stationary Navier-Stokes equations is investigated. The effect is of a different nature than the one shown for the non-stationary case by J. Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier. Existence of a unique solution is shown for arbitrary large external force provided the Coriolis force is large enough. The analysis is carried out in a new framework of the Fourier-Besov spaces. In addition to the stationary case counterparts of several classical results for the non-stationary Navier-Stokes problem have been proven.