Stochastic quasi-geostrophic equation

Details Stochastic quasi-geostrophic equation Stochastic quasi-geostrophic equation

2011-08-24

arxiv.org/abs/1108.4896v1

Mathematics

Probability

Scientific paper

In this note we study the 2d stochastic quasi-geostrophic equation in $\mathbb{T}^2$ for general parameter $\alpha\in (0,1)$ and multiplicative noise. We prove the existence of martingale solutions and pathwise uniqueness under some condition in the general case, i.e. for all $\alpha\in (0,1)$. In the subcritical case $\alpha>1/2$, we prove existence and uniqueness of (probabilistically) strong solutions and construct a Markov family of solutions. In particular, it is uniquely ergodic for $\alpha>2/3$ provided the noise is non-degenerate. In this case, the convergence to the (unique) invariant measure is exponentially fast. In the general case, we prove the existence of Markov selections.

Affiliated with

Also associated with

No associations

Rating

Stochastic quasi-geostrophic equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stochastic quasi-geostrophic equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic quasi-geostrophic equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-377924