REDUCED DISSIPATION EFFECT IN STOCHASTIC TRANSPORT BY GAUSSIAN NOISE WITH REGULARITY GREATER THAN 1/2 - Archive ouverte HAL Access content directly
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REDUCED DISSIPATION EFFECT IN STOCHASTIC TRANSPORT BY GAUSSIAN NOISE WITH REGULARITY GREATER THAN 1/2

Abstract

Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE which in certain cases represents the equation for the mean value. From this equation we observe a reduced dissipation property with respect to delta correlated noise when regularity is higher than the one of Brownian motion, a fact interpreted qualitatively here as a signature of the reduced dissipation observed for 2D turbulent fluids due to the inverse cascade. We give results also for the variance of the solution and for a scaling limit of a two-component noise input.
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hal-04108818 , version 1 (28-05-2023)

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Franco Flandoli, Francesco Russo. REDUCED DISSIPATION EFFECT IN STOCHASTIC TRANSPORT BY GAUSSIAN NOISE WITH REGULARITY GREATER THAN 1/2. 2023. ⟨hal-04108818⟩
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