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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
On the stochastic selection of integral curves of a rough vector field
Jules Pitcho
We prove that for bounded, divergence-free vector fields b in L^1_{loc}((0,1];BV(\T^d;\R^d)), there exists a unique incompressible measure on integral curves of b. We recall the ve…
math.AP2024
On the lack of selection for the transport equation over a dense set of vector fields
Jules Pitcho
We construct a set of bounded vector fields dense in for and with for which smooth regu…