On vanishing diffusivity selection for the advection equation

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-01-21 DOI:10.1007/s10231-025-01543-6

Giulia Mescolini, Jules Pitcho, Massimo Sorella

引用次数: 0

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 \(L^1_{loc}((0,T];BV(\mathbb {T}^d;\mathbb {R}^d))\cap L^2((0,T) \times \mathbb {T}^d;\mathbb {R}^d))\), 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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关于平流方程的消失扩散系数选择

我们研究了沿初始奇异矢量场的平流方程。更确切地说，我们证明了\(L^1_{loc}((0,T];BV(\mathbb {T}^d;\mathbb {R}^d))\cap L^2((0,T) \times \mathbb {T}^d;\mathbb {R}^d))\)中无散度向量场存在唯一的消失扩散解。这类包括了depow在[13]中构造的向量场，对于这个向量场，平流方程有无穷多个不同的有界解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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