Advances in Applied Probability

Probabilistic methods for the incompressible Navier‒Stokes equations with space periodic conditions

G. N. Milstein and M. V. Tretyakov

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Abstract

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

Article information

Source
Adv. in Appl. Probab., Volume 45, Number 3 (2013), 742-772.

Dates
First available in Project Euclid: 30 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1377868537

Digital Object Identifier
doi:10.1239/aap/1377868537

Mathematical Reviews number (MathSciNet)
MR3102470

Zentralblatt MATH identifier
1280.35097

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 65M25: Method of characteristics 65M12: Stability and convergence of numerical methods 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Probabilistic representations of solutions of partial differential equations Feynman‒Kac formula weak approximation of stochastic differential equations layer method Helmholtz‒Hodge decomposition

Citation

Milstein, G. N.; Tretyakov, M. V. Probabilistic methods for the incompressible Navier‒Stokes equations with space periodic conditions. Adv. in Appl. Probab. 45 (2013), no. 3, 742--772. doi:10.1239/aap/1377868537. https://projecteuclid.org/euclid.aap/1377868537


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