, Volume 266, Issue 3, pp 631-645

A Stochastic Perturbation of Inviscid Flows

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Abstract

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a C k local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as ν   → 0, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$ .

Communicated by A. Kupiainen