Orthogonal decompositions and bases for three-dimensional vector fields

DOI10.1080/01630569408816576zbMath0806.46016OpenAlexW1976875643MaRDI QIDQ4302532

J. F. G. Auchmuty

Publication date: 4 October 1994

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569408816576

zbMATH Keywords

spectral expansionHelmholtz decomposition\mathbb{R}^ 3)\)3-dimensional vector fields on nice domains in spaceeigenproblems involving the scalar and vector LaplacianHodge-Weyl decomposition of fields in \(L^ 2(\Omegavariational construction of potentials

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (7)

The S.V.D. of the Poisson kernel ⋮ A Helmholtz/Weyl decomposition in energy space ⋮ Bounds and representations of solutions of planar div-curl problems ⋮ Finite-energy solutions of mixed 3d div-curl systems ⋮ A symmetric weak form of Biot's equations based on redundant variables representing the fluid, using a Helmholtz decomposition of the fluid displacement vector field ⋮ Poloidal-Toroidal Decomposition of Solenoidal Vector Fields in the Ball ⋮ Divergence L ²-Coercivity Inequalities

Cites Work

• The method of orthogonal projection in potential theory
• On Helmholtz’s decomposition theorem and Poisson’s equation with an infinite domain
• Finite Element Methods for Navier-Stokes Equations
• Some Remarks on Rellich's Theorem and the Poincaré Inequality
• On Regularity of the Boundary in the Theory of Sobolev Spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Orthogonal decompositions and bases for three-dimensional vector fields