非局部相互作用漩涡

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-09 DOI:10.1137/23m1563438

Margherita Solci

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3430-3451 页，2024 年 6 月。摘要。我们考虑了取决于一个小参数[math]的二次非局部函数序列，它们通过 Bourgain、Brezis 和 Mironescu 的一个著名结果逼近了 Dirichlet 积分。与狄利克特积分中涡旋能量的核心半径近似方法类似，我们进一步用[math]来标度这些能量，并将它们限制为[math]值函数。我们引入了一个函数收敛到积分电流的概念，与之相对，这些能量是等价的，并展示了对涡旋能量的收敛，这与金兹堡-朗道能量在涡旋缩放时的极限行为类似。

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Nonlocal-Interaction Vortices

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3430-3451, June 2024.
Abstract. We consider sequences of quadratic nonlocal functionals, depending on a small parameter [math], that approximate the Dirichlet integral by a well-known result by Bourgain, Brezis, and Mironescu. Similarly to what is done for core-radius approximations to vortex energies in the case of the Dirichlet integral, we further scale such energies by [math] and restrict them to [math]-valued functions. We introduce a notion of convergence of functions to integral currents with respect to which such energies are equicoercive, and show the convergence to a vortex energy, similarly to the limit behavior of Ginzburg–Landau energies at the vortex scaling.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.