Publication

On vanishing diffusivity selection for the advection equation

Giulia Mescolini
2025

Abstract

We study the advection equation along vector fields singular at the initial time. More precisely, we prove that for divergence-free vector fields in $L_{\text{loc}}^1((0,T]; BV(\mathbb{T}^d; \mathbb{R}^d)) \cap L^2((0,T) \times \mathbb{T}^d; \mathbb{R}^d)$ , there exists a unique vanishing diffusivity solution. This class includes the vector field constructed by Depauw in [13], for which there are infinitely many distinct bounded solutions to the advection equation.

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Giulia Mescolini
2025

Abstract

Official source

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On vanishing diffusivity selection for the advection equation

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