Unique Ergodicity in Stochastic Electroconvection

TL;DR

This paper investigates a stochastic electroconvection model, proving solution existence and uniqueness, analyzing its Markov properties, and establishing conditions for a unique smooth invariant measure.

Contribution

It introduces a stochastic electroconvection model, proving well-posedness and invariant measure uniqueness under certain noise conditions.

Findings

Existence and uniqueness of solutions established.

Markov semigroup and Feller properties analyzed.

Unique smooth invariant measure proven under sufficient noise.

Abstract

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller properties. When the noise forces enough modes in phase space, we obtain the uniqueness of the smooth invariant measure for the Markov transition kernels associated with the model.