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

Z. Brzeźniak, B. Goldys and Quoc Thong Le Gia

Abstract

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

Keywords: stochastic Navier–Stokes equation, rotating sphere, random dynamical sytem, asymptotic compactness.

AMS Subject Classification: Primary 35R60; secondary 35Q30, 60H15, 76D06, 76M35.