Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

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 eq...

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Bibliographic Details
Published in:Advances in applied probability 2013-09, Vol.45 (3), p.742-772
Main Authors: Milstein, G. N., Tretyakov, M. V.
Format: Article
Language:English
Subjects:
35Q30
60H30
65M12
65M25
Approximation
Boundary conditions
Differential equations
Feynman‒Kac formula
General Applied Probability
Helmholtz‒Hodge decomposition
Human error
layer method
Mathematical analysis
Mathematical models
Navier Stokes equation
Navier-Stokes equations
Numerical methods
Probabilistic methods
Probabilistic representations of solutions of partial differential equations
Probability
Probability distribution
Probability theory
Representations
Scalars
Spectral methods
Stochastic models
Studies
Viscosity
weak approximation of stochastic differential equations
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Summary: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.
ISSN:0001-8678
1475-6064
DOI:10.1239/aap/1377868537