EQUATION REGISTRY

Helmholtz decomposition

Decaying fields on all space or compatible boundaries; harmonic components require separate conditions.

Theory · FOUNDATIONEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-SD-001
u=uL+uT,∇×uL=0,∇⋅uT=0\mathbf u=\mathbf u_L+\mathbf u_T,\quad\nabla\times\mathbf u_L=0,\quad\nabla\cdot\mathbf u_T=0

Decaying fields on all space or compatible boundaries; harmonic components require separate conditions.
Chapter reference: Ch. 4 (4.5) · ASD-BOOK-ddbade997b45

Source and ID

ASD-WEB-SD-001 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

Return to premises and derivation
Adopted source, conditions and previous versions

Ch. 4 (4.5)

Registered formula checked individually against the final manuscript; The mathematical content agrees; the existing expression and its derivation conditions are retained.

Conditions retained in this adoption

  • Decaying fields on all space or compatible boundaries; harmonic components require separate conditions.

Source locators: p1317

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

Download source identity manifest

The manifest identifies the source; it is not the complete manuscript. Adopting this source does not upgrade evidence or grant a new licence.

Previous source, retained as history

SD-51779505a476 · Ch. 4 (4.5)

DEPENDS ON

Dependencies

No preceding equation is recorded in this index. Consult the source topic for definitions, geometry and model scope.

USED BY

Uses of this equation

Subsequent equationFourier projectorsASD-WEB-SD-002Subsequent equationCompression-positive densityASD-WEB-SD-003Subsequent equationQuadratic continuum actionASD-WEB-SD-005DocumentContinuum Degrees of FreedomDocumentSpace Dynamics Foundation
Discuss this page Browse all equations