The stochastic quasi-geostrophic equation
Seminar Room 1, Newton Institute
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.