关于平流方程的消失扩散系数选择

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

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引用次数: 0

摘要

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。

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On vanishing diffusivity selection for the advection equation

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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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

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.