Year: 2026
Type: preprint
Abstract: We use the Laplacian in n-dimensional spherical coordinates (n>1) to write the divergence of a vector field defined on radially symmetric domains in the context of vector calculus. We apply straightforward equations of vector calculus with the nabla operator and the transformation matrices from Cartesian to spherical polar coordinates. One needs the divergence of a vector field e.g. to prove that vector fields are eigenfunctions of the Stokes operator on n-dimensional annuli and balls. Our divergence formula in partial derivatives in n-dimensional spherical polar coordinates is an important step in a future verification of further Stokes eigenfunctions on those domains.
Source: arXiv (Cornell University)
Authors: Rummler, Bernd, Thäter, Gudrun
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167056065
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