Stochastic Navier--Stokes equations on a 3D thin domain

Zdzisław Brzeźniak; Gaurav Dhariwal; Quoc Thong Le Gia

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arXiv · 2008.07394

Stochastic Navier--Stokes equations on a 3D thin domain

Zdzisław Brzeźniak·Gaurav Dhariwal·Quoc Thong Le Gia

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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.

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Zdzisław Brzeźniak, Gaurav Dhariwal, Quoc Thong Le Gia. 2020-08-17. Stochastic Navier--Stokes equations on a 3D thin domain. https://arxiv.org/abs/2008.07394

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