Possible effect of noise on stretching mechanism

摘要

To understand the possible effect of random perturbations on stretching mechanism we investigate a very simplified model where a passive vector field, like a magnetic field, is transported and stretched by an a priori given velocity field, which is perturbed by noise. Without noise perturbation there are examples of bounded measurable velocity field which induces a singularity of a certain degree: the passive field is not locally square integrable, for positive times, although the initial condition is smooth. With noise, the solution remains at least summable of any order.