Abstract
Exponential mixing for the 2D stochastic damped Euler equation driven by bounded noise
We study the two-dimensional stochastic damped Euler equation on the torus driven by bounded random forcing. Under sufficiently strong damping, we establish a unique invariant measure and exponential mixing for the associated discrete time Markov semigroup. The key ingredient is a global in time $W^{1,infty}$ estimate for the vorticity, which yields tightness for the construction of an invariant measure and enable a synchronous argument for exponential convergence to equilibrium. We also obtain a corresponding result for sufficiently small noise at any fixed positive damping. This is joint work with Chunrong Feng and Huaizhong Zhao.