Splitting up method for the 2d stochastic navier–stokes equations

被引：10
作者：
Bessaih H. [1 ]
Brzeźniak Z. [2 ]
Millet A. [3 ,4 ]
机构：
[1] Department of Mathematics, University of Wyoming, Dept. 3036, 1000 East University Avenue, Laramie, 82071, WY
[2] Department of Mathematics, University of York, Heslington, York
[3] SAMM, EA 4543, Université Paris 1 Panthéon-Sorbonne, 90 Rue de Tolbiac, Paris Cedex
[4] Laboratoire de Probabilités et Modèles Aléatoires, Universités Paris 6-Paris 7, Boîte Courrier 188, 4 place Jussieu, Paris Cedex 05
来源：
Stochastic Partial Differential Equations: Analysis and Computations | 2014年 / 2卷 / 4期
关键词：
Hydrodynamical models; Navier; Speed of convergence in probability; Splitting up methods; Stochastic PDEs; Stokes equations; Strong convergence;
D O I：
10.1007/s40072-014-0041-7
中图分类号：
学科分类号：
摘要：
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier–Stokes equations on the torus suggested by the Lie–Trotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given for periodic boundary conditions. In particular, we prove that the strong speed of the convergence in probability is almost 1/2. This is shown by means of an L2 (Ω, ℙ) convergence localized on a set of arbitrary large probability. The assumptions on the diffusion coefficient depend on the fact that some multiple of the Laplace operator is present or not with the multiplicative stochastic term. Note that if one of the splitting steps only contains the stochastic integral, then the diffusion coefficient may not contain any gradient of the solution. © Springer Science+Business Media New York 2014.
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页码：433 / 470
页数：37
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