Stationary solutions for the fractional Navier-Stokes-Coriolis system in Fourier-Besov spaces

TL;DR

This paper establishes the existence and stability of stationary solutions for the three-dimensional fractional Navier-Stokes-Coriolis system within Fourier-Besov spaces, linking external forces and Coriolis effects.

Contribution

It introduces new results on stationary solutions in critical Fourier-Besov spaces for the fractional Navier-Stokes-Coriolis system, including stability and uniqueness conditions.

Findings

Existence of stationary solutions in Fourier-Besov spaces.

Stability of non-stationary solutions converging to stationary ones.

Conditions linking external force and Coriolis parameter for uniqueness.

Abstract

In this work we prove the existence of stationary solutions for the tridimensional fractional Navier-Stokes- Coriolis in critical Fourier-Besov spaces. We first deal with the non-stationary fractional Navier-Stokes-Coriolis and in this framework we get the existence of stationary solutions. Also we state a kind of stability of these non-stationary solutions which applied to the stationary case permits to conclude that, under suitable conditions, non-stationary solutions converge to the stationary ones when the time goes to infinity. Finally we establish a relation between the external force and the Coriolis parameter in order to get a unique solution for the stationary system.