Helmholtz-Hodge Decompositions in the Nonlocal Framework: Well-Posedness Analysis and Applications
Helmholtz-Hodge Decompositions in the Nonlocal Framework: Well-Posedness Analysis and Applications
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非局部框架中的 Helmholtz-Hodge 分解：适定性分析与应用
DOI：
10.1007/s42102-020-00035-w
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Yu, Yue
中科院分区：
文献类型：
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作者：
D’Elia, Marta;Flores, Cynthia;Li, Xingjie;Radu, Petronela;Yu, Yue
出现在各种物理模型中的非局域算子满足恒等式，并享有与经典对应算子相似的一系列性质。本文得到了三个分量的两点向量场的Helmholtz-Hodge分解，其中三个分量的非局部旋度为零，非局部散度为零，第三个分量为(非局部)无旋度且无散度的分量。所得到的结果包含了不同的非局部边界条件，因此适用于各种情况。
Nonlocal operators that have appeared in a variety of physical models satisfy identities and enjoy a range of properties similar to their classical counterparts. In this paper, we obtain Helmholtz-Hodge type decompositions for two-point vector fields in three components that have zero nonlocal curls, zero nonlocal divergence, and a third component which is (nonlocally) curl-free and divergence-free. The results obtained incorporate different nonlocal boundary conditions, thus being applicable in a variety of settings.