SPD

Abstract

In this talk we talk about the 2D stochastic quasi-geostrophic equation on T2 for general parameter  2 (0; 1) and multiplicative noise. We prove the existence of martingale solutions and Markov selections for multiplicative noise for all  2 (0; 1) . In the subcritical case  > 1=2, we prove existence and uniqueness of (probabilistically) strong solutions. We obtain the ergodicity for  > 1=2 for degenerate noise. We also study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on T2 driven by real linear multiplicative noise and additive noise in the subcritical case by proving the existence of a random attractor. 1