Exponential convergence of the stochastic micropolar and magneto-micropolar fluid systems
Kazuo Yamazaki · Communications on Stochastic Analysis · 2016
We study the micropolar and magneto-micropolar fluid systems with random forces in two-dimensional case.The additional terms on the equations that govern the time evolution of the velocity and micro-rotational velocity vector fields are more singular than many other equations that have been previously studied, for example Bénard or magnetic Bénard problem.Following the approach of [2] via a coupling method, we prove the existence and uniqueness of their solutions and the invariant measures as well as the exponential convergence of its trajectories to the unique invariant measure.