@Article{NMTMA-13-1,
author = {Zhao, Wenju and Max, Gunzburger},
title = {Auxiliary Equations Approach for the Stochastic Unsteady  Navier-Stokes Equations with Additive Random Noise},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2020},
volume = {13},
number = {1},
pages = {1--26},
abstract = {<p style="text-align: justify;">This paper presents a Martingale regularization method for the stochastic Navier-Stokes equations with additive noise. The original system is split into two equivalent parts, the linear stochastic Stokes equations with Martingale solution and the stochastic modified Navier-Stokes equations with relatively-higher regularities. Meanwhile, a fractional Laplace operator is introduced to regularize the noise term. The stability and convergence of numerical scheme for the pathwise modified Navier-Stokes equations are proved.&nbsp;The comparisons of non-regularized and regularized noises for the Navier-Stokes system are numerically presented to further demonstrate the efficiency of our numerical scheme.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0055},
url = {https://global-sci.com/article/90335/auxiliary-equations-approach-for-the-stochastic-unsteady-navier-stokes-equations-with-additive-random-noise}
}