A stochastic perturbation of inviscid flows

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 $\holderspace{k}α$ 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 $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.

13 pages, no figures.

References in corpus (1)

• A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations

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