Random attractor associated with the quasi-geostrophic equation

Abstract

We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on ${\mathbb{T}}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha >1/2$) by proving the existence of a random attractor. The key point for the proof is the exponential decay of the $L^p$-norm and a boot-strapping argument. The upper semicontinuity of random attractors is also established. Moreover, if the viscosity constant is large enough, the system has a trivial random attractor.

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Random attractors for a class of stochastic partial differential equations driven by general additive noise