Stochastic Lagrangian Particle Approach to Fractal Navier-Stokes Equations

A Stochastic-lagrangian Particle System for the Navier-stokes Equations

Abstract. This paper is based on a formulation of the Navier-Stokes equations developed in arxiv:math.PR/0511067 (to appear in Commun. Pure Appl. Math), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take N copies of the above process (each based on independent Wiener processes), and replace the expected val...

An Eulerian-Lagrangian approach to the Navier-Stokes equations

We present a formulation of the incompressible viscous Navier-Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

0 An Eulerian - Lagrangian Approach to the Navier - Stokes equations

Stochastic Navier-stokes Equations

1. Stochastic Integration on Hilbert spaces 2 1.1. Gaussian measures on Hilbert spaces 2 1.2. Wiener processes on Hilbert spaces 6 1.3. Martingales on Banach spaces 7 1.4. Stochastic integration 8 1.5. Appendix: Stochastic integration w.r.t. cylindrical Wiener processes 12 2. Stochastic Di erential Equations on Hilbert spaces 13 2.1. Mild, weak and strong solutions 13 2.2. Existence and uniquen...

A Stochastic-lagrangian Approach to the Navier-stokes Equations in Domains with Boundary

In this paper we derive a probabilistic representation of the deterministic 3-dimensional Navier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in CPAM, 2008. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One notable feature of the formulation in the...