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math.AP2024
Self-similar instability and forced nonuniqueness: an application to the 2D Euler equations
Michele Dolce, Giulia Mescolini
Building on an approach introduced by Golovkin in the '60s, we show that nonuniqueness in some forced PDEs is a direct consequence of the existence of a self-similar linearly unsta…
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…