Back to Search Start Over

Anomalous Regularization in Kazantsev-Kraichnan Model

Authors :
Bagnara, Marco
Grotto, Francesco
Maurelli, Mario
Publication Year :
2024

Abstract

This work investigates a passive vector field which is transported and stretched by a divergence-free Gaussian velocity field, delta-correlated in time and poorly correlated in space (spatially nonsmooth). Although the advection of a scalar field (Kraichnan's passive scalar model) is known to enjoy regularizing properties, the potentially competing stretching term in vector advection may induce singularity formation. We establish that the regularization effect is actually retained in certain regimes. While this is true in any dimension $d\ge 3$, it notably implies a regularization result for linearized 3D Euler equations with stochastic modeling of turbulent velocities, and for the induction equation in magnetohydrodynamic turbulence.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2411.09482
Document Type :
Working Paper