Communications in Mathematical Physics

, Volume 266, Issue 3, pp 631–645

A Stochastic Perturbation of Inviscid Flows

Authors

    • Department of MathematicsUniversity of Chicago
Article

DOI: 10.1007/s00220-006-0058-5

Cite this article as:
Iyer, G. Commun. Math. Phys. (2006) 266: 631. doi:10.1007/s00220-006-0058-5

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

Copyright information

© Springer-Verlag 2006