Preprints, Working Papers, ... Year : 2025

On vanishing diffusivity for the advection equation

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 $L^1 loc ((0, T ];BV(\T^d;\R^d))\cap L^2((0,T)\times\T^d;\R^d)$, there exists a unique vanishing diffusivity solution. This class includes the vector field constructed by Depauw, for which there are infinitely many distinct bounded solutions to the advection equation.
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Dates and versions

ensl-04811722 , version 1 (29-11-2024)

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Giulia Mescolini, Jules Pitcho, Massimo Sorella. On vanishing diffusivity for the advection equation. 2024. ⟨ensl-04811722v1⟩
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