Random dynamical systems generated by stochastic Navier--Stokes equation on the rotating sphere

TL;DR

This paper establishes the existence and uniqueness of solutions to stochastic Navier--Stokes equations on a rotating sphere and demonstrates the formation of an asymptotically compact random dynamical system.

Contribution

It provides the first rigorous proof of solution existence and uniqueness for stochastic Navier--Stokes equations on a rotating sphere and constructs the related random dynamical system.

Findings

Existence and uniqueness of solutions proven.

Asymptotic compactness of the associated random dynamical system shown.

Abstract

In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system associated with the equations.