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

Eduard Feireisl; Madalina Petcu

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

Analysis of PDEs 2026-07-05 v1

Authors: Eduard Feireisl , Madalina Petcu

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.

Keywords

data assimilation Oberbeck-Boussinesq system stochastic problems convergence relative energy inequality

Cite

@article{arxiv.2607.04458,
  title  = {A continuous data assimilation method for a variant of Oberbeck-Boussinesq system with randomly perturbed data},
  author = {Eduard Feireisl and Madalina Petcu},
  journal= {arXiv preprint arXiv:2607.04458},
  year   = {2026}
}