We consider a stochastic system of N particles, usually called vortices in that setting,
approximating the 2D Navier–Stokes equation written in vorticity. Assuming that the initial …

We introduce, on some examples, the main tools to analyze the convergence rate of
stochastic particle methods for the numerical approximation of some nonlinear parabolic …

In these lectures we shall concentrate on certain mathematical results concerning the case
of deterministic Euler and stochastic Navier-Stokes equations for incompressible fluids. For …

The main purpose of this work is to provide a Hilbertian functional framework for the analysis
of the planar incompressible Navier–Stokes (NS) equations either in vorticity or in stream …

In this paper, we give a probabilistic interpretation of a viscous scalar conservation law in a
bounded interval thanks to a nonlinear martingale problem. The underlying nonlinear …

We develop a probabilistic interpretation of local mild solutions of the three dimensional
Navier-Stokes equation in the L p spaces, when the initial vorticity field is integrable. This is …

We give a probabilistic representation for the solution to a nonlinear evolution equation
induced by a measure-valued branching process. We first construct the involved branching …

A novel probabilistic scheme for solving the incompressible Navier-Stokes equations is
studied, in which we approximate a generalized nonlinear Feyman-Kac formula. The …

PROBABILISTIC INTERPRETATION AND PARTICLE METHOD FOR VORTEX EQUATIONS
WITH NEUMANN’S BOUNDARY CONDITION Page 1 Proceedings of the Edinburgh …

For some parabolic equations with a local nonlinearity, a suitable spatial derivation leads to
a Fokker-Planck equation with a nonlocal nonlinearity. In this paper we present a review of …