Large-domain stability of random attractors for stochastic g-Navier–Stokes equations with additive noise

Abstract

Abstract This paper concerns the long term behavior of the stochastic two-dimensional g-Navier–Stokes equations with additive noise defined on a sequence of expanding domains, where the ultimate domain is unbounded and of Poincaré type. We prove that the weak continuity is uniform with respect to all expanding cocycles, which yields the equi-asymptotic compactness by using an energy equation method. Finally, we show the existence of a random attractor for the equation on each domain and the upper semi-continuity of random attractors as the bounded domain is expanded to the unbounded ultimate domain.

Keywords

• Stochastic g-Navier–Stokes
• Expanding domains
• Expanding cocycles
• Energy equation method
• Equi-asymptotic compactness
• Upper semi-continuity