Stochastic Constrained Navier-Stokes Equations on \(\mathbb{T}^2\)

We study constrained 2-dimensional Navier-Stokes Equations driven by a multiplicative Gaussian noise in the Stratonovich form. In the deterministic case [4] we showed the existence of global solutions only on a two dimensional torus and hence we concentrated on such a case here. We prove the existen...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Authors: Brzeźniak, Zdzisław, Dhariwal, Gaurav
Format: Article
Language:English
Subjects:
Fluid dynamics
Fluid flow
Martingales
Mathematical analysis
Navier-Stokes equations
Random noise
Toruses
Online Access:Get full text
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Summary:We study constrained 2-dimensional Navier-Stokes Equations driven by a multiplicative Gaussian noise in the Stratonovich form. In the deterministic case [4] we showed the existence of global solutions only on a two dimensional torus and hence we concentrated on such a case here. We prove the existence of a martingale solution and later using Schmalfuss idea [20] we show the pathwise uniqueness of the solutions. We also establish the existence of a strong solution using a Yamada-Watanabe type result from Ondrej\'{a}t [17].
ISSN:2331-8422