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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Veröffentlicht in:	Advances in applied probability 2013-09, Vol.45 (3), p.742-772
Hauptverfasser:	Milstein, G. N., Tretyakov, M. V.
Format:	Artikel
Sprache:	eng
Schlagworte:	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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Beschreibung
Zusammenfassung:	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