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arXiv · 1908.08624

Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications

M. D'Elia·C. Flores·X. Li·P. Radu·Y. Yu
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Abstract

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.

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M. D'Elia, C. Flores, X. Li, P. Radu, Y. Yu. 2019-08-22. Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications. https://arxiv.org/abs/1908.08624

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