On vanishing diffusivity selection for the advection equation
| Autor: | Mescolini, Giulia, Pitcho, Jules, Sorella, Massimo |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the advection equation along vector fields singular at the initial time. More precisely, we prove that for divergence-free vector fields in $L^1_{loc}((0, T ]; BV (\mathbb{T}^d;\mathbb{R}^d))\cap L^2((0, T ) \times\mathbb{T}^d;\mathbb{R}^d)$, there exists a unique vanishing diffusivity solution. This class includes the vector field constructed by Depauw, for which there are infinitely many distinct bounded solutions to the advection equation. Comment: Comments are welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|