EQUATION REGISTRY

Nonnegative free-field energy

Positive coefficients give nonnegative quadratic energy; zero modes and boundaries still need specification.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-SD-009
E2=12ρs∣∂tu∣2+12KL(∇⋅u)2+12KT∣∇×u∣2≥0\mathcal E_2=\tfrac12\rho_s|\partial_t\mathbf u|^2+\tfrac12K_L(\nabla\cdot\mathbf u)^2+\tfrac12K_T|\nabla\times\mathbf u|^2\ge0

Positive coefficients give nonnegative quadratic energy; zero modes and boundaries still need specification.
Chapter reference: Ch. 4 (4.10) · ASD-BOOK-ddbade997b45

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Ch. 4 (4.10)

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

  • Positive coefficients give nonnegative quadratic energy; zero modes and boundaries still need specification.

Source locators: p1329

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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SD-51779505a476 · Ch. 4 (4.10)

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