A Stochastic Perturbation of Inviscid Flows |
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Authors: | Gautam Iyer |
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Institution: | (1) Department of Mathematics, University of Chicago, Chicago, Illinois 60637, USA |
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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 C
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 → 0, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of
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