2020
DOI: 10.48550/arxiv.2007.08838
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Sufficient conditions for local scaling laws for stationary martingale solutions to the 3D Navier-Stokes equations

Stavros Papathanasiou

Abstract: The main goal of this paper is to obtain sufficient conditions that allow us to rigorously derive local versions of the 4/5 and 4/3 laws of hydrodynamic turbulence, by which we mean versions of these laws that hold in bounded domains. This is done in the context of stationary martingale solutions of the Navier-Stokes equations driven by an Ornstein-Uhlenbeck process. Specifically, we show that under an assumption of "on average" precompactness in L 3 , the local structure functions are expressed up to first or… Show more

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