Volume 13, Issue 1
Auxiliary Equations Approach for the Stochastic Unsteady Navier--Stokes Equations with Additive Random Noise

Wenju Zhao and Max Gunzburger

10.4208/nmtma.OA-2019-0055

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 1-26.

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  • Abstract

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. 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.


  • History

Published online: 2019-12

  • AMS Subject Headings

35R60, 65Mxx, 76Dxx

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