无发散矢量场的流函数

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
J. Kelliher
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引用次数: 2

摘要

1990年,von Wahl和Borchers和Sohr分别证明了与边界相切的三维有界域中的无散度矢量场u u可以写成在域边界上消失的矢量场的旋度。我们将这一结果推广到更高维和Lipschitz边界,以一种适用于平面空间积分的形式,表明u u可以写成反对称矩阵场的散度。我们还证明了获得这样一个矩阵域的核与获得该域的Biot-Savart核是对偶的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stream functions for divergence-free vector fields
In 1990, von Wahl and, independently, Borchers and Sohr showed that a divergence-free vector field u u in a 3D bounded domain that is tangential to the boundary can be written as the curl of a vector field vanishing on the boundary of the domain. We extend this result to higher dimension and to Lipschitz boundaries in a form suitable for integration in flat space, showing that u u can be written as the divergence of an antisymmetric matrix field. We also demonstrate how obtaining a kernel for such a matrix field is dual to obtaining a Biot-Savart kernel for the domain.
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来源期刊
Quarterly of Applied Mathematics
Quarterly of Applied Mathematics 数学-应用数学
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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