A continuous data assimilation method for a variant of Oberbeck-Boussinesq system with randomly perturbed data

Abstract

We show convergence of a continuous data assimilation method for the Oberbeck-Boussinesq system in the dimension $d=2,3$. Our working hypothesis is boundedness of the reference solution, while the synchronized solution satisfies the equations in a weak sense. The main tool is the relative energy inequality for stochastic problems.