An elementary approach to mixing and dissipation enhancement by transport noise

2024/02/12 by Luo, Dejun, Tang, Bin, Zhao, Guohuan · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2402.07484

Abstract

We investigate the mixing properties of solutions to the stochastic transport equation d u= ∘ d W ⋅∇ u, where the driving noise W(t,x) is white in time, colored and divergence-free in space. Furthermore, we prove the dissipation enhancement in the presence of a small viscous term. Applying our results, we also derive the mixing properties for a regularized stochastic 2D Euler equation.

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