Article

Communications in Mathematical Physics

, Volume 266, Issue 3, pp 631-645

First online:

A Stochastic Perturbation of Inviscid Flows

  • Gautam IyerAffiliated withDepartment of Mathematics, University of Chicago Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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 \(O(\sqrt{\nu t})\).