Noise prevents infinite stretching of the passive field in a stochastic vector advection equation

Abstract

A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Hölder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.

23 pages, 4 figures

References in corpus (2)

• Noise Prevents Singularities in Linear Transport Equations
• Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

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• Stochastic Variational Formulations of Fluid Wave-Current Interaction
• Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations