A stochastic perturbation of inviscid flows

الأصل · EN

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 kα 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(√νt).