4 papers
Non-selection of Lagrangian trajectories in the zero-noise limit for a class of stochastic regularizations
Lucio Galeati, Filippo Giovagnini, Massimo Sorella
We prove the lack of selection in the zero-noise limit for solutions to SDEs driven by a divergence-free, Hölder continuous vector field with exponent , arbitrarily clos…
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…
Non-uniqueness of parabolic solutions for advection-diffusion equation
Thérèse Moerschell, Massimo Sorella
We present a novel example of a divergence-free velocity field for arbitrary but fixed which leads to non-unique solutions of adv…
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…