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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.AP2024
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…