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A stochastic perturbation of inviscid flows

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

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Gautam Iyer. 2010-03-15. A stochastic perturbation of inviscid flows. https://doi.org/10.1007/s00220-006-0058-5

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