Convergence of the random vortex method.(English)Zbl 0635.35077

An approximate solution of the Cauchy problem for the incompressible Navier-Stokes equations in two space dimensions is constructed by means of a modified random vortex method. The main result is the following convergence theorem: if the initial vorticity distribution $$\omega$$ (x,0)$$\in S$$ (the Schwartz class), then with high probability this method produces good approximations to the true velocity.
Reviewer: J.R.Romanovsky

MSC:

 35Q30 Navier-Stokes equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J65 Brownian motion 76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

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