Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate

Details Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate

2008-09-29

arxiv.org/abs/0809.4947v4

Annals of Applied Probability 2010, Vol. 20, No. 5, 1761-1800

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP672 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP672

We develop a McKean-Vlasov interpretation of Navier-Stokes equations with external force field in the whole space, by associating with local mild $L^p$-solutions of the 3d-vortex equation a generalized nonlinear diffusion with random space-time birth that probabilistically describes creation of rotation in the fluid due to nonconservativeness of the force. We establish a local well-posedness result for this process and a stochastic representation formula for the vorticity in terms of a vector-weighted version of its law after its birth instant. Then we introduce a stochastic system of 3d vortices with mollified interaction and random space-time births, and prove the propagation of chaos property, with the nonlinear process as limit, at an explicit pathwise convergence rate. Convergence rates for stochastic approximation schemes of the velocity and the vorticity fields are also obtained. We thus extend and refine previous results on the probabilistic interpretation and stochastic approximation methods for the nonforced equation, generalizing also a recently introduced random space-time-birth particle method for the 2d-Navier-Stokes equation with force.

Affiliated with

Also associated with

No associations

Rating

Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic vortex method for forced three-dimensional Navier--Stokes equations and pathwise convergence rate will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-49136