Stochastic Constrained Navier-Stokes Equations on $\mathbb{T}^2$
Analysis of PDEs
2018-01-11 v3 Probability
Abstract
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].
Cite
@article{arxiv.1701.01385,
title = {Stochastic Constrained Navier-Stokes Equations on $\mathbb{T}^2$},
author = {Zdzisław Brzeźniak and Gaurav Dhariwal},
journal= {arXiv preprint arXiv:1701.01385},
year = {2018}
}
Comments
37 pages, Edited Abstract, removed typos, Corrected proof of Lemma 5.3