Stochastic Navier--Stokes equations on a 3D thin domain
Probability
2020-08-18 v1 Analysis of PDEs
Abstract
Stochastic Navier--Stokes equations in a thin three-dimensional domain are considered, driven by additive noise. The convergence of martingale solution of the stochastic Navier--Stokes equations in a thin three-dimensional domain to the unique martingale solution of the 2D stochastic Navier--Stokes equations, as the thickness of the film vanishes, is established. Hence, we justify the approximation of 3D Navier--Stokes equations driven by random forcing by its corresponding two-dimensional setting in applications.
Cite
@article{arxiv.2008.07394,
title = {Stochastic Navier--Stokes equations on a 3D thin domain},
author = {Zdzisław Brzeźniak and Gaurav Dhariwal and Quoc Thong Le Gia},
journal= {arXiv preprint arXiv:2008.07394},
year = {2020}
}
Comments
46 pages. Dedicated to the memory of Igor D. Chueshov