Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball

DOI10.1134/S1990478919030098zbMath1438.42049OpenAlexW2970698497WikidataQ127311090 ScholiaQ127311090MaRDI QIDQ4973183

V. B. Kardakov, Sergeĭ Gavrilovich Kazantsev

Publication date: 2 December 2019

Published in: Journal of Applied and Industrial Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1990478919030098

zbMATH Keywords

Mie representationZernike polynomialsolenoidaltoroidal and poloidal vector fieldsvector spherical harmonic

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximation by polynomials (41A10) Other special orthogonal polynomials and functions (33C47) Spherical harmonics (33C55)

Related Items (2)

Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields ⋮ Singular value decomposition of the longitudinal ray transform of vector fields in a ball in cone beam coordinates

Cites Work

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• Spherical harmonics and approximations on the unit sphere. An introduction
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• Spherical harmonics
• $L^r$-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains
• Finite Element Methods for Navier-Stokes Equations
• Decomposition Theorems for Solenoidal Vector Fields
• Orthogonal decompositions and bases for three-dimensional vector fields
• Kinematic dynamos in spheroidal geometries
• BASIC SYSTEMS FOR THE GEOMAGNETIC FIELD
• Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

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