We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid dynamical equations with transport noise to deterministic viscous equations. Quantitative estimates on the convergence rates are provided by combining analytic and probabilistic arguments, especially heat kernel properties and maximal estimates for stochastic convolutions. Similar ideas are applied to the stochastic 2D Keller-Segel model, yielding explicit choice of noise to ensure that the blow-up probability is less than any given threshold. Our approach also gives rise to some mixing property for stochastic linear transport equations and dissipation enhancement in the viscous case.

Quantitative convergence rates for scaling limit of SPDEs with transport noise

Flandoli, Franco;Galeati Lucio;Luo Dejun
2024

Abstract

We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid dynamical equations with transport noise to deterministic viscous equations. Quantitative estimates on the convergence rates are provided by combining analytic and probabilistic arguments, especially heat kernel properties and maximal estimates for stochastic convolutions. Similar ideas are applied to the stochastic 2D Keller-Segel model, yielding explicit choice of noise to ensure that the blow-up probability is less than any given threshold. Our approach also gives rise to some mixing property for stochastic linear transport equations and dissipation enhancement in the viscous case.
2024
Settore MAT/06 - Probabilita' e Statistica Matematica
Transport noise; Scaling limit; Convergence rate; Mixing; Dissipation enhancement; Stochastic convolution
   Noise in Fluids
   NoisyFluid
   European Commission
   Horizon Europe Framework Programme
   101053472
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/138822
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