3 papers
math.PR2025
On the zero-noise limit for SDE's singular at the initial time
Jules Pitcho
We investigate the zero-noise limit for SDE's driven by Brownian motion with a divergence-free drift singular at the initial time and prove that a unique probability measure concen…
math.AP2024
On vanishing diffusivity selection for the advection equation
Giulia Mescolini, Jules Pitcho, Massimo Sorella
We study the advection equation along vector fields singular at the initial time. More precisely, we prove that for divergence-free vector fields in $L^1_{loc}((0, T ]; BV (\mathbb…
math.AP2021
Almost everywhere non-uniqueness of integral curves for divergence-free Sobolev vector fields
J. Pitcho, M. Sorella
We construct divergence-free Sobolev vector fields in C([0,1];W^{1,r}(T^d;R^d)) with r < d and d >=2 which simultaneously admit any finite number of distinct positive solutions to…