Invariant Measures for a Stochastic Electroconvection Model

TL;DR

This paper studies a stochastic electroconvection model, proving existence, uniqueness, and invariant measures for the system, contributing to the understanding of nonlinear surface charge dynamics under randomness.

Contribution

It introduces a new stochastic electroconvection model and establishes fundamental properties like solution existence, uniqueness, and invariant measures.

Findings

Existence and uniqueness of solutions confirmed.

The Markov semigroup is shown to be weak Feller.

Invariant measures for the model are established.

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 and we show that the corresponding Markov semigroup is weak Feller. We also prove the existence of invariant measures for the Markov transition kernels associated with the model.