Quantitative convergence rates for scaling limit of SPDEs with transport noise

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.

arXiv comment34 pages

References in corpus (6)

• Stochastic integration in UMD Banach spaces
• Suppression of chemotactic explosion by mixing
• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
• Dissipation Enhancement by Mixing
• Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes
• Eddy heat exchange at the boundary under white noise turbulence

Cited by in corpus (5)

• On the Boussinesq hypothesis for a stochastic Proudman-Taylor model
• No blow-up by nonlinear Itô noise for the Euler equations
• Dissipation enhancement by transport noise for stochastic $p$-Laplace equations
• Scaling Limits of Stochastic Transport Equations on Manifolds
• Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow